List of Publications
List of Publications
C.-W. Shu,
Mathematics of Computation, v49 (1987), pp.105-121.
C.-W. Shu,
TVB boundary treatment for numerical solutions of
conservation laws,
Mathematics of Computation,
v49 (1987), pp.123-134.
C.-W. Shu,
Total-variation-diminishing time discretizations,
SIAM Journal on Scientific and Statistical Computing, v9
(1988), pp..
C.-W. Shu and S. Osher,
Efficient implementation of essentially
non-oscillatory shock-capturing schemes,
Journal of Computational Physics, v77 (1988), pp.439-471.
B. Cockburn and C.-W. Shu,
TVB Runge-Kutta local projection discontinuous
Galerkin finite element method for conservation laws II:
general framework,
Mathematics of
Computation, v52 (1989), pp.411-435.
C.-W. Shu and S. Osher,
Efficient implementation of essentially non-
oscillatory shock-capturing schemes II,
Journal of Computational Physics, v83 (1989), pp.32-78.
B. Cockburn, S.-Y. Lin and C.-W. Shu,
TVB Runge-Kutta local projection discontinuous
Galerkin finite element method for conservation laws III:
one-dimensional systems,
Journal of Computational Physics, v84 (1989), pp.90-113.
W. Cai, D. Gottlieb and C.-W. Shu,
Essentially nonoscillatory spectral Fourier methods
for shock wave calculations,
Mathematics of Computation, v52 (1989), pp.389-410.
B. Cockburn, S. Hou and C.-W. Shu,
Galerkin finite element method for conservation laws IV:
the multidimensional case,
Mathematics of Computation, v54 (1990), pp.545-581.
C.-W. Shu,
Numerical experiments on the accuracy of ENO and
modified ENO schemes, Journal of Scientific Computing,
v5 (1990), pp.127-149.
B. Cockburn and C.-W. Shu,
The Runge-Kutta local projection P1-discontinuous-Galerkin
finite element method for scalar conservation laws,
Mathematical Modelling and Numerical
Analysis (M^2 AN), v25 (1991), pp.337-361.
S. Osher and C.-W. Shu,
High-order essentially nonoscillatory schemes for
Hamilton-Jacobi equations,
SIAM Journal
on Numerical Analysis, v28 (1991), pp.907-922.
C.-W. Shu,
A numerical method for systems of conservation laws
of mixed type admitting hyperbolic flux splitting,
Journal of Computational Physics v100 (1992), pp.424-429.
C.-W. Shu, T.A. Zang, G. Erlebacher, D. Whitaker and S. Osher,
High-order ENO schemes applied to two- and three-dimensional
compressible flow,
Applied Numerical Mathematics,
v9 (1992), pp.45-71.
W. Cai, D. Gottlieb and C.-W. Shu,
On one-sided filters for spectral Fourier
approximations of discontinuous functions,
SIAM Journal on Numerical Analysis v29 (1992), pp.905-916.
D. Chen, E.C. Kan, U. Ravaioli, C.-W. Shu and R.W. Dutton,
An improved energy transport model including
nonparabolicity and non-Maxwellian distribution effects,
IEEE Electron Device Letters, v13 (1992), pp.26-28.
D. Gottlieb, C.-W. Shu, A. Solomonoff and H. Vandeven,
On the Gibbs phenomenon I: recovering exponential
accuracy from the Fourier partial sum of a nonperiodic
analytic function,
Journal of Computational
and Applied Mathematics, v43 (1992), pp.81-98.
W. Cai and C.-W. Shu,
Uniform high-order spectral methods for one- and
two-dimensional Euler equations,
Journal of Computational Physics, v104 (1993), pp.427-443.
W. E and C.-W. Shu,
Effective equations and the inverse cascade theory for
Kolmogorov flows,
Physics of Fluids A, v5 (1993), pp.998-1010.
W. E and C.-W. Shu,
A numerical resolution study of high order
essentially non-oscillatory schemes applied to incompressible
Journal of
Computational Physics, v110 (1994), pp.39-46.
B. Cockburn and C.-W. Shu,
Nonlinearly stable compact schemes for shock
calculations,
SIAM Journal on Numerical Analysis, v31 (1994), pp.607-627.
G. Jiang and C.-W. Shu,
On a cell entropy inequality for discontinuous Galerkin
Mathematics of Computation, v62 (1994), pp.531-538.
W. E and C.-W. Shu,
Small-scale structures in
Boussinesq convection,
Physics of Fluids, v6 (1994), pp.49-58.
J. Casper, C.-W. Shu and H. Atkins,
Comparison of two formulations for high-order
accurate essentially nonoscillatory schemes,
AIAA Journal, v32 (1994), pp..
D. Gottlieb and C.-W. Shu,
Resolution properties of the Fourier method for
discontinuous waves,
Methods in Applied Mechanics and Engineering, v116 (1994), pp.27-37.
Z. Chen, B. Cockburn, J.W. Jerome and C.-W. Shu,
Mixed-RKDG finite element methods for the 2-D hydrodynamic model
for semiconductor device simulation,
VLSI Design, v3 (1995), pp.145-158.
J.W. Jerome and C.-W. Shu,
The response of the hydrodynamic model to heat
conduction, mobility, and relaxation expressions,
VLSI Design, v3 (1995), pp.131-143.
D. Gottlieb and C.-W. Shu,
On the Gibbs phenomenon IV: recovering exponential accuracy in
a subinterval from a Gegenbauer partial sum of a piecewise
analytic function,
Mathematics of Computation, v64 (1995), pp..
C.-W. Shu and P.S. Wong,
A note on the accuracy of spectral method applied to nonlinear
conservation laws,
Journal of Scientific Computing, v10 (1995), pp.357-369.
J. Jerome and C.-W. Shu,
Transport effects and characteristic modes in the modeling and
simulation of submicron devices,
IEEE Transactions on Computer-Aided Design of Integrated Circuits and
Systems, v14 (1995), pp.917-923.
D. Gottlieb and C.-W. Shu,
On the Gibbs phenomenon V: recovering exponential accuracy
from collocation point values of a piecewise
analytic function,
Numerische Mathematik, v71 (1995), pp.511-526.
D.P. Chen, R.S. Eisenberg, J.W. Jerome and C.-W. Shu,
Hydrodynamic model of temperature change in open ionic channels,
Biophysical Journal, v69 (1995), pp..
D. Gottlieb and C.-W. Shu,
On the Gibbs phenomenon III: recovering exponential accuracy in
a sub-interval from a spectral partial sum of a piecewise
analytic function,
SIAM Journal on Numerical Analysis, v33 (1996), pp.280-290.
B. Perthame and C.-W. Shu,
On positive preserving finite volume schemes for
Euler equations,
Numerische Mathematik, v73 (1996), pp.119-130.
E. Harabetian, S. Osher and C.-W. Shu,
An Eulerian approach for vortex motion using a level set regularization
procedure,
Journal of Computational Physics, v127 (1996), pp.15-26.
G.-S. Jiang and C.-W. Shu,
Efficient implementation of weighted ENO schemes,
Journal of Computational Physics, v126 (1996), pp.202-228.
C.-W. Shu and Y. Zeng,
High order essentially non-oscillatory scheme for viscoelasticity
with fading memory,
Quarterly of Applied Mathematics, v55 (1997), pp.459-484.
G. Erlebacher, M.Y. Hussaini and C.-W. Shu,
Interaction of a shock with a longitudinal vortex,
Journal of Fluid Mechanics, v337 (1997), pp.129-153.
D. Gottlieb and C.-W. Shu,
On the Gibbs phenomenon and its resolution,,
SIAM Review, v30 (1997), pp.644-668.
K. Siddiqi, B.B. Kimia and C.-W. Shu,
Geometric shock-capturing ENO schemes for subpixel interpolation,
computation and curve evolution,,
Models and Image Processing (CVGIP:GMIP), v59 (1997), pp.278-301.
S. Gottlieb and C.-W. Shu,
Total variation diminishing Runge-Kutta schemes,
Mathematics of Computation, v67 (1998), pp.73-85.
B. Cockburn and C.-W. Shu,
The Runge-Kutta discontinuous Galerkin method for conservation laws V:
multidimensional systems,
Journal of Computational Physics, v141 (1998), pp.199-224.
H.L. Atkins and C.-W. Shu,
Quadrature-free implementation of discontinuous Galerkin method
for hyperbolic equations,
AIAA Journal, v36 (1998), pp.775-782.
G.-Q. Chen, J.W. Jerome and C.-W. Shu,
Analysis and simulation of extended hydrodynamic models:
the multi-valley Gunn oscillator and MESFET symmetries,
VLSI Design, v6 (1998), pp.277-282.
C. Cercignani, I.M. Gamba, J.W. Jerome and C.-W. Shu,
Applicability of the high field model:
an analytical study via asymptotic parameters defining domain
decomposition,
VLSI Design, v8 (1998), pp.135-141.
C. Cercignani, I.M. Gamba, J.W. Jerome and C.-W. Shu,
Applicability of the high field model:
a preliminary numerical study,
VLSI Design, v8 (1998), pp.275-282.
B. Cockburn and C.-W. Shu,
The local discontinuous Galerkin method for time-dependent
convection-diffusion systems,
SIAM Journal on Numerical Analysis, v35 (1998), pp..
P. Montarnal and C.-W. Shu,
Real gas computation using an energy relaxation method and high-order
WENO schemes,
Journal of Computational Physics, v148 (1999), pp.59-80.
C. Hu and C.-W. Shu,
Weighted essentially non-oscillatory schemes on triangular meshes,
Journal of Computational Physics, v150 (1999), pp.97-127.
C. Hu and C.-W. Shu,
A discontinuous Galerkin finite element method for Hamilton-Jacobi
equations,
SIAM Journal on Scientific Computing, v21 (1999), pp.666-690.
O. Lepsky, C. Hu and C.-W. Shu,
SIAM Review,
v43 (2001), pp.89-112.
T. Zhou, Y. Guo and C.-W. Shu,
Numerical study on Landau damping
Physica D, v157 (2001), pp.322-333.
A. Arnold, J.A. Carrillo, I. Gamba and C.-W. Shu,
Low and high field scaling limits for the Vlasov- and
Wigner-Poisson-Fokker-Planck systems
Transport Theory and Statistical Physics,
v30 (2001), pp.121-153.
T. Zhou, Y. Li and C.-W. Shu,
Numerical comparison of WENO finite volume and Runge-Kutta
discontinuous Galerkin methods
Journal of Scientific Computing,
v16 (2001), pp.145-171.
B. Cockburn and C.-W. Shu,
Runge-Kutta Discontinuous Galerkin methods for convection-dominated
Journal of Scientific Computing,
v16 (2001), pp.173-261.
M.A. Anile, J.A. Carrillo, I.M. Gamba and C.-W. Shu,
Approximation of the BTE by a relaxation-time operator:
simulations for a 50nm-channel Si diode
VLSI Design
v13 (2001), pp.349-354.
K. Banoo, J.-H. Rhew, M. Lundstrom, C.-W. Shu and J.W. Jerome,
Simulating quasi-ballistic transport in Si nanotransistors
VLSI Design
v13 (2001), pp.5-13.
J. Shi, C. Hu and C.-W. Shu,
A technique of treating negative weights in WENO schemes
Journal of Computational Physics, v175 (2002), pp.108-127.
J. Yan and C.-W. Shu,
A local discontinuous Galerkin method for KdV type equations
SIAM Journal on Numerical Analysis, v40 (2002), pp.769-791.
J. Yan and C.-W. Shu,
Local discontinuous Galerkin methods for partial
differential equations with higher order derivatives
Journal of Scientific Computing, v17 (2002), pp.27-47.
J.A. Carrillo, I.M. Gamba, A. Majorana and C.-W. Shu,
A WENO-solver for the 1D non-stationary Boltzmann-Poisson system
for semiconductor devices
Journal of Computational Electronics, v1 (2002), pp.365-370.
P. Lin and C.-W. Shu,
Numerical solution of a virtual internal bond model for material
Physica D, v167 (2002), pp.101-121.
J. Qiu and C.-W. Shu,
On the construction, comparison, and local characteristic
decomposition for high-order central WENO schemes
Journal of Computational Physics, v183 (2002), pp.187-209.
G.-D. Jin, D.-Y. Liu and C.-W. Shu,
Propagation and decay of concentration wave in the liquid-solid
pulsed fluidized beds
The Chinese Journal of Process Engineering (in Chinese),
v2 (2002), pp.392-399.
C.-W. Shu,
High-order finite difference and finite volume WENO schemes
and discontinuous Galerkin methods for CFD
International Journal of Computational Fluid Dynamics,
v17 (2003), pp.107-118.
B. Cockburn, M. Luskin, C.-W. Shu and E. Suli,
Enhanced accuracy by post-processing for finite element methods for
hyperbolic equations
Mathematics of Computation, v72 (2003), pp.577-606.
M.H. Carpenter, D. Gottlieb and C.-W. Shu,
On the conservation and convergence to weak solutions of global schemes
Journal of Scientific Computing, v18 (2003), pp.111-132.
Y.-T. Zhang and C.-W. Shu,
High order WENO schemes for Hamilton-Jacobi equations on triangular meshes
SIAM Journal on Scientific Computing, v24 (2003), pp..
J.A. Carrillo, I.M. Gamba, A. Majorana and C.-W. Shu,
A WENO-solver for the transients of Boltzmann-Poisson system for
semiconductor devices: performance and comparisons with Monte Carlo methods
Journal of Computational Physics, v184 (2003), pp.498-525.
R.P. Fedkiw, G. Sapiro and C.-W. Shu,
Shock capturing, level sets, and PDE based methods in computer vision
and image processing: a review of Osher's contributions
Journal of Computational Physics, v185 (2003), pp.309-341.
K. Sebastian and C.-W. Shu,
Multidomain WENO finite difference method with
interpolation at subdomain interfaces
Journal of Scientific Computing, v19 (2003), pp.405-438.
M. Zhang and C.-W. Shu,
An analysis of three different formulations of the discontinuous Galerkin method for
diffusion equations
Mathematical Models and Methods in Applied Sciences, v13 (2003), pp.395-413.
J. Shi, Y.-T. Zhang and C.-W. Shu,
Resolution of high order WENO schemes for complicated flow structures
Journal of Computational Physics, v186 (2003), pp.690-696.
J. Qiu and C.-W. Shu,
Finite difference WENO schemes with Lax-Wendroff-type time discretizations
SIAM Journal on Scientific Computing, v24 (2003), pp..
M. Zhang, C.-W. Shu, G.C.K. Wong and S.C. Wong,
A weighted essentially non-oscillatory numerical scheme for a
multi-class Lighthill-Whitham-Richards traffic flow model
Journal of Computational Physics, v191 (2003), pp.639-659.
Y.-T. Zhang, J. Shi, C.-W. Shu and Y. Zhou,
Numerical viscosity and resolution of high-order
weighted essentially nonoscillatory
schemes for compressible flows with high Reynolds numbers
Physical Review E, v68 (2003), 046709.
J. Qiu and C.-W. Shu,
Hermite WENO schemes and their application as limiters for
Runge-Kutta discontinuous Galerkin method: one dimensional case
Journal of Computational Physics, v193 (2003), pp.115-135.
J.A. Carrillo, I.M. Gamba, A. Majorana and C.-W. Shu,
A direct solver for 2D non-stationary Boltzmann-Poisson systems
for semiconductor devices: a MESFET simulation by WENO-Boltzmann schemes
Journal of Computational Electronics, v2 (2003), pp.375-380.
J. Ryan and C.-W. Shu,
On a one-sided post-processing technique for the discontinuous
Galerkin methods
Methods and Applications of Analysis, v10 (2003),
pp.295-308.
Q. Zhang, M. Zhang, G. Jin, D. Liu and C.-W. Shu,
Modeling, numerical methods,
and simulation for particle-fluid two-phase flow problems
Computers and Mathematics with Applications, v47 (2004), pp..
Y. Guo, C.-W. Shu and T. Zhou,
The dynamics of a plane diode
SIAM Journal on Mathematical Analysis, v35 (2004), pp..
B. Cockburn, F. Li and C.-W. Shu,
Locally divergence-free
discontinuous Galerkin methods for the Maxwell equations
Journal of Computational Physics, v194 (2004), pp.588-610.
Q. Zhang and C.-W. Shu,
Error estimates to smooth solutions of Runge-Kutta
discontinuous Galerkin methods for scalar conservation laws
SIAM Journal on Numerical Analysis, v42 (2004), pp.641-666.
D. Levy, C.-W. Shu and J. Yan,
Local discontinuous Galerkin methods for nonlinear dispersive equations
Journal of Computational Physics, v196 (2004), pp.751-772.
Y. Xu and C.-W. Shu,
Local discontinuous Galerkin methods for three classes of nonlinear wave equations
Journal of Computational Mathematics, v22 (2004), pp.250-274.
L.-L. Feng, C.-W. Shu and M. Zhang,
A hybrid cosmological hydrodynamic/N-body code based on a weighted
essentially nonoscillatory scheme
Astrophysical Journal, v612 (2004), pp.1-13.
Y. Liu and C.-W. Shu,
Local discontinuous Galerkin methods for moment models
in device simulations: formulation and one dimensional results
Journal of Computational Electronics, v3 (2004), pp.263-267.
F. Li and C.-W. Shu,
Locally divergence-free discontinuous Galerkin methods for MHD equations
Journal of Scientific Computing, v22-23 (2005), pp.413-442.
M. Zhang and C.-W. Shu,
An analysis of and a comparison between the discontinuous
Galerkin and the spectral finite volume methods
Computers and Fluids, v34 (2005), pp.581-592.
Y. Ha, C.L. Gardner, A. Gelb and C.-W. Shu,
Numerical simulation of high Mach number astrophysical jets with radiative cooling
Journal of Scientific Computing, v24 (2005), pp.597-612.
C.-W. Shu, W.-S. Don, D. Gottlieb, O. Schilling and L. Jameson,
Numerical convergence study of nearly incompressible, inviscid Taylor-Green vortex flow
Journal of Scientific Computing, v24 (2005), pp.569-595.
J. Ryan, C.-W. Shu and H. Atkins,
Extension of a postprocessing technique for the discontinuous
Galerkin method for hyperbolic equations with application to
an aeroacoustic problem
SIAM Journal on Scientific Computing, v26 (2005), pp.821-843.
J. Qiu and C.-W. Shu,
Runge-Kutta discontinuous Galerkin method using WENO limiters
SIAM Journal on Scientific Computing, v26 (2005), pp.907-929.
J. Qiu and C.-W. Shu,
Hermite WENO schemes and their application as limiters for
Runge-Kutta discontinuous Galerkin method II: two dimensional case
Computers and Fluids, v34 (2005), pp.642-663.
J. Qiu and C.-W. Shu,
Hermite WENO schemes for Hamilton-Jacobi equations
Journal of Computational Physics, v204 (2005), pp.82-99.
F. Li and C.-W. Shu,
Reinterpretation and simplified implementation of
a discontinuous Galerkin method for Hamilton-Jacobi equations
Applied Mathematics Letters, v18 (2005), pp..
Y. Xu and C.-W. Shu,
Local discontinuous Galerkin methods for nonlinear Schrodinger equations
Journal of Computational Physics, v205 (2005), pp.72-97.
S. Chen, W. E and C.-W. Shu,
The heterogeneous multiscale method based on the discontinuous
Galerkin method for hyperbolic and parabolic problems
Multiscale Modeling and Simulation, v3 (2005), pp.871-894.
Z. Xu and C.-W. Shu,
Anti-diffusive flux corrections for high order finite difference WENO schemes
Journal of Computational Physics, v205 (2005), pp.458-485.
J. Qiu, M. Dumbser and C.-W. Shu,
The discontinuous Galerkin method with Lax-Wendroff type time
discretizations
Computer Methods in Applied Mechanics and Engineering,
v194 (2005), pp..
Y. Xing and C.-W. Shu,
High order finite difference WENO schemes with the exact conservation
property for the shallow water equations
Journal of Computational Physics, v208 (2005), pp.206-227.
L.-L. Feng, P. He, L. Fang, C.-W. Shu and M. Zhang,
Intergalactic medium in the $\Lambda$CDM universe from cosmological
simulations
Journal of the Korean Astronomical Society,
v38 (2005), pp.129-132.
F. Filbet and C.-W. Shu,
Approximation of hyperbolic models for chemosensitive movement
SIAM Journal on Scientific Computing, v27 (2005), pp.850-872.
J. Qiu and C.-W. Shu,
A comparison of troubled-cell indicators for
Runge-Kutta discontinuous Galerkin methods using weighted
essentially nonoscillatory limiters
SIAM Journal on Scientific Computing, v27 (2005), pp.995-1013.
Y. Xu and C.-W. Shu,
Local discontinuous Galerkin methods for two classes of two-dimensional
nonlinear wave equations
Physica D, v208 (2005), pp.21-58.
S. Zhang, Y.-T. Zhang and C.-W. Shu,
Multistage interaction of a shock wave and a strong vortex
Physics of Fluids, v17 (2005), 116101.
F. Filbet, Y. Guo and C.-W. Shu,
Analysis of the relativistic Vlasov-Maxwell model in an interval
Quarterly of Applied Mathematics, v63 (2005), pp.691-714.
Z. Xu and C.-W. Shu,
Anti-diffusive high order WENO schemes for Hamilton-Jacobi equations
Methods and Applications of Analysis, v12 (2005), pp.169-190.
Y. Xu and C.-W. Shu,
Local discontinuous Galerkin methods for the Kuramoto-Sivashinsky
equations and the Ito-type coupled KdV equations
Computer Methods in Applied Mechanics and Engineering, v195 (2006),
J. Qiu, B.C. Khoo and C.-W. Shu,
A numerical study for the performance of the Runge-Kutta
discontinuous Galerkin method based on different numerical fluxes
Journal of Computational Physics, v212 (2006), pp.540-565.
P. Zhang, S.C. Wong and C.-W. Shu,
A weighted essentially non-oscillatory numerical scheme for a multi-class
traffic flow model on an inhomogeneous highway
Journal of Computational Physics, v212 (2006), pp.739-756.
J.A. Carrillo, I.M. Gamba, A. Majorana and C.-W. Shu,
2D semiconductor device simulations by WENO-Boltzmann schemes:
efficiency, boundary conditions and comparison to Monte Carlo methods
Journal of Computational Physics, v214 (2006), pp.55-80.
Y. Xing and C.-W. Shu,
High-order well-balanced finite difference WENO schemes for a class
of hyperbolic systems with source terms
Journal of Scientific Computing, v27 (2006), pp.477-494.
Y. Xing and C.-W. Shu,
High order well-balanced finite volume WENO schemes and discontinuous Galerkin
methods for a class of hyperbolic systems with source terms
Journal of Computational Physics, v214 (2006), pp.567-598.
Y. Xing and C.-W. Shu,
A new approach of high order well-balanced finite volume WENO
schemes and discontinuous Galerkin methods for a class of
hyperbolic systems with source terms
Communications in Computational Physics, v1 (2006), pp.101-135.
S. Gottlieb, D. Gottlieb and C.-W. Shu,
Recovering high-order accuracy in WENO computations of steady-state hyperbolic systems
Journal of Scientific Computing, v28 (2006), pp.307-318.
C.-S. Chou and C.-W. Shu,
High order residual distribution conservative finite difference WENO
schemes for steady state problems on non-smooth meshes
Journal of Computational Physics, v214 (2006), pp.698-724.
K. Kremeyer, K. Sebastian and C.-W. Shu,
Computational study of shock mitigation and drag reduction by pulsed energy lines,
AIAA Journal, v44 (2006), pp..
P. He, J. Liu, L.-L. Feng, C.-W. Shu and L.-Z. Fang,
Low-redshift cosmic baryon fluid on large scales and She-Leveque universal scaling
Physical Review Letters, v96 (2006), 051302.
L. Yuan and C.-W. Shu,
Discontinuous Galerkin method based on non-polynomial
approximation spaces
Journal of Computational Physics, v218 (2006), pp.295-323.
Z. Xu and C.-W. Shu,
Anti-diffusive finite difference WENO methods for shallow water
with transport of pollutant
Journal of Computational Mathematics, v24 (2006), pp.239-251.
Y.-T. Zhang, C.-W. Shu and Y. Zhou,
Effects of shock waves on Rayleigh-Taylor instability
Physics of Plasmas, v13 (2006), 062705.
J.-M. Qiu, C.-W. Shu, L.-L. Feng and L.-Z. Fang,
A WENO algorithm for the radiative transfer and ionized sphere at reionization
New Astronomy, v12 (2006), pp.1-10.
Q. Zhang and C.-W. Shu,
Error estimates to smooth solutions of Runge-Kutta discontinuous
Galerkin method for symmetrizable systems of conservation laws
SIAM Journal on Numerical Analysis, v44 (2006), pp..
Y. Xing and C.-W. Shu,
Application of high order well-balanced schemes to a class of
hyperbolic systems with source terms
Boletin de la Sociedad Espanola de Matematica Aplicada,
v34 (2006), pp.69-80.
S. Zhang, Y.-T. Zhang and C.-W. Shu,
Interaction of an oblique shock wave with a pair of parallel vortices:
shock dynamics and mechanism of sound generation
Physics of Fluids, v18 (2006), 126101.
D. Levy, S. Nayak, C.-W. Shu and Y.-T. Zhang,
Central WENO schemes for Hamilton-Jacobi equations on triangular meshes
SIAM Journal on Scientific Computing, v28 (2006), pp..
M.J. Caceres, J.A. Carrillo, I. Gamba, A. Majorana and C.-W. Shu,
DSMC versus WENO-BTE: a double gate MOSFET example
Journal of Computational Electronics, v5 (2006), pp.471-474.
F. Li and C.-W. Shu,
A local-structure-preserving local discontinuous Galerkin
method for the Laplace equation
Methods and Applications of Analysis, v13 (2006), pp.215-234.
Y. Liu and C.-W. Shu,
Local discontinuous Galerkin methods for moment models in device simulations:
performance assessment and two dimensional results
Applied Numerical Mathematics, v57 (2007), pp.629-645.
S. Zhang and C.-W. Shu,
A new smoothness indicator for the WENO schemes and its
effect on the convergence to steady state solutions
Journal of Scientific Computing, v31 (2007), pp.273-305.
Y. Cheng and C.-W. Shu,
A discontinuous Galerkin finite element method for
directly solving the Hamilton-Jacobi equations
Journal of Computational Physics, v223 (2007), pp.398-415.
J. Shen, C.-W. Shu and M. Zhang,
High resolution schemes for a hierarchical size-structured model
SIAM Journal on Numerical Analysis, v45 (2007), pp.352-370.
C.-S. Chou and C.-W. Shu,
High order residual distribution conservative finite difference WENO
schemes for convection-diffusion steady state problems on non-smooth meshes
Journal of Computational Physics, v224 (2007), pp.992-1020.
Y. Xu and C.-W. Shu,
Error estimates of the semi-discrete local discontinuous Galerkin
method for nonlinear convection-diffusion and KdV equations
Computer Methods in Applied Mechanics and Engineering,
v196 (2007), pp..
J.-M. Qiu, L.-L. Feng, C.-W. Shu and L.-Z. Fang,
A WENO algorithm of the temperature and ionization profiles around a point source
New Astronomy, v12 (2007), pp.398-409.
Y. Liu, C.-W. Shu, E. Tadmor and M. Zhang,
Non-oscillatory hierarchical reconstruction for central
and finite volume schemes
Communications in Computational Physics, v2 (2007), pp.933-963.
Y. Xia, Y. Xu and C.-W. Shu,
Efficient time discretization for local discontinuous Galerkin methods
Discrete and Continuous Dynamical Systems - Series B,
v8 (2007), pp.677-693.
S. Chen, W. E, Y. Liu and C.-W. Shu,
A discontinuous Galerkin implementation of a
domain decomposition method for kinetic-hydrodynamic coupling
multiscale problems in gas dynamics and device simulations
Journal of Computational Physics, v225 (2007), pp..
J. Liu, J.-M. Qiu, L.-L. Feng, C.-W. Shu and L.-Z. Fang,
21 cm signals from early ionizing sources
The Astrophysical Journal, v663 (2007), pp.1-9.
S. Noelle, Y. Xing and C.-W. Shu,
High-order well-balanced finite volume WENO schemes for
shallow water equation with moving water
Journal of Computational Physics, v226 (2007), pp.29-58.
Y. Xia, Y. Xu and C.-W. Shu,
Local discontinuous Galerkin methods for the Cahn-Hilliard type equations
Journal of Computational Physics, v227 (2007), pp.472-491.
J. Shen, C.-W. Shu and M. Zhang,
A high order WENO scheme for a hierarchical size-structured population model
Journal of Scientific Computing, v33 (2007), pp.279-291.
J. Cheng and C.-W. Shu,
A high order ENO conservative Lagrangian type scheme for the compressible Euler equations
Journal of Computational Physics, v227 (2007), pp..
S. Curtis, R.M. Kirby, J.K. Ryan and C.-W. Shu,
Postprocessing for the discontinuous Galerkin method over nonuniform meshes
SIAM Journal on Scientific Computing, v30 (2007), pp.272-289.
Y. Liu, C.-W. Shu, E. Tadmor and M. Zhang,
Central discontinuous Galerkin methods on overlapping cells
with a nonoscillatory hierarchical reconstruction
SIAM Journal on Numerical Analysis, v45 (2007), pp..
J. Cheng and C.-W. Shu,
A high order accurate conservative remapping method on staggered meshes
Applied Numerical Mathematics, v58 (2008), pp..
Y. Cheng and C.-W. Shu,
A discontinuous Galerkin finite element method for time dependent
partial differential equations with higher order derivatives
Mathematics of Computation, v77 (2008), pp.699-730.
Y. Xu and C.-W. Shu,
A local discontinuous Galerkin method for the Camassa-Holm equation
SIAM Journal on Numerical Analysis, v46 (2008), pp..
J.-M. Qiu and C.-W. Shu,
Convergence of Godunov-type schemes for scalar conservation laws
under large time steps
SIAM Journal on Numerical Analysis, v46 (2008), pp..
J.-M. Qiu, C.-W. Shu, J.-R. Liu and L.-Z. Fang,
A WENO algorithm for the growth of ionized regions at the reionization epoch
New Astronomy, v13 (2008), pp.1-11.
L. Yuan and C.-W. Shu,
Discontinuous Galerkin method for a class of elliptic multi-scale problems
International Journal for Numerical Methods in Fluids, v56 (2008), pp..
W. Chen, S.C. Wong and C.-W. Shu,
Efficient implementation of the shock-fitting algorithm for the
Lighthill-Whitham-Richards traffic flow model
International Journal for Numerical Methods in Engineering,
v74 (2008), pp.554-600.
Y. Lu, S.C. Wong, M. Zhang, C.-W. Shu and W. Chen,
Explicit construction of entropy solutions for the Lighthill-Whitham-Richards
traffic flow model with a piecewise quadratic flow-density relationship
Transportation Research Part B, v42 (2008), pp.355-372.
Y. Liu, C.-W. Shu and M. Zhang,
Strong stability preserving property of the deferred correction time discretization
Journal of Computational Mathematics, v26 (2008), pp.633-656.
W. Wang, X. Li and C.-W. Shu,
The discontinuous Galerkin method for the multiscale modeling of dynamics
of crystalline solids
Multiscale Modeling and Simulation,
v7 (2008), pp.294-320.
J. Zhu, J. Qiu, C.-W. Shu and M. Dumbser,
Runge-Kutta discontinuous Galerkin method using WENO limiters II: unstructured meshes
Journal of Computational Physics, v227 (2008), pp..
Y. Liu, C.-W. Shu, E. Tadmor and M. Zhang,
$L^2$ stability analysis of the central discontinuous Galerkin method
and a comparison between the central and regular discontinuous Galerkin methods
ESAIM: Mathematical Modelling and Numerical Analysis (M^2 AN),
v42 (2008), pp.593-607.
Y. Xia, S.C. Wong, M. Zhang, C.-W. Shu and W.H.K. Lam,
An efficient discontinuous Galerkin method on triangular meshes for a pedestrian flow model
International Journal for Numerical Methods in Engineering,
v76 (2008), pp.337-350.
J. Cheng and C.-W. Shu,
A third order conservative Lagrangian type scheme on
curvilinear meshes for the compressible Euler equations
Communications in Computational Physics, v4 (2008), pp..
L. Huang, C.-W. Shu and M. Zhang,
Numerical boundary conditions for the fast sweeping high order WENO
methods for solving the Eikonal equation
Journal of Computational Mathematics, v26 (2008), pp.336-346.
Y. Cheng, I.M. Gamba, A. Majorana and C.-W. Shu,
Discontinuous Galerkin solver for Boltzmann-Poisson transients
Journal of Computational Electronics, v7 (2008), pp.119-123.
S. Zhang, S. Jiang and C.-W. Shu,
Development of nonlinear weighted compact schemes with increasingly higher order accuracy
Journal of Computational Physics, v227 (2008), pp..
F. Li, C.-W. Shu, Y.-T. Zhang and H. Zhao,
A second order discontinuous Galerkin fast sweeping method for Eikonal equations
Journal of Computational Physics, v227 (2008), pp..
J.-M. Qiu and C.-W. Shu,
Convergence of high order finite volume weighted essentially non-oscillatory
scheme and discontinuous Galerkin method for nonconvex conservation laws
SIAM Journal on Scientific Computing, v31 (2008), pp.584-607.
Y. Cheng and C.-W. Shu,
Superconvergence and time evolution of discontinuous Galerkin finite element solutions
Journal of Computational Physics, v227 (2008), pp..
Y. Xu and C.-W. Shu,
Local discontinuous Galerkin method for the Hunter-Saxton
equation and its zero-viscosity and zero-dispersion limits
SIAM Journal on Scientific Computing, v31 (2008), pp..
C.-W. Shu,
High order weighted essentially nonoscillatory schemes for
convection dominated problems
SIAM Review, v51 (2009), pp.82-126.
Y.-T. Zhang and C.-W. Shu,
Third order WENO scheme on three dimensional tetrahedral meshes
Communications in Computational Physics, v5 (2009), pp.836-848.
Y. Xia, Y. Xu and C.-W. Shu,
Application of the local discontinuous Galerkin method for the
Allen-Cahn/Cahn-Hilliard system
Communications in Computational Physics, v5 (2009), pp.821-835.
R. Abgrall and C.-W. Shu,
Development of residual distribution schemes for the discontinuous
Galerkin method: the scalar case with linear elements
Communications in Computational Physics, v5 (2009), pp.376-390.
L. Huang, S.C. Wong, M. Zhang, C.-W. Shu and W.H.K. Lam,
Revisiting Hughes' dynamic continuum model for pedestrian flow and
the development of an efficient solution algorithm
Transportation Research Part B, v43 (2009), pp.127-141.
W. Wang and C.-W. Shu,
The WKB local discontinuous Galerkin method for the simulation of
Schrodinger equation in a resonant tunneling diode
Journal of Scientific Computing, v40 (2009), pp.360-374.
S. Gottlieb, D.I. Ketcheson and C.-W. Shu,
High order strong stability preserving time discretizations
Journal of Scientific Computing, v38 (2009), pp.251-289.
L. Huang, Y. Xia, S.C. Wong, C.-W. Shu, M. Zhang and W.H.K. Lam,
Dynamic continuum model for bi-directional pedestrian flows
Proceedings of the Institution of Civil Engineers:
Engineering and Computational Mechanics, v162 (2009), pp.67-75.
Y. Cheng and C.-W. Shu,
Superconvergence of local discontinuous Galerkin methods for one-dimensional convection-diffusion equations
Computers and Structures, v87 (2009), pp.630-641.
Z. Xu, Y. Liu and C.-W. Shu,
Hierarchical reconstruction for discontinuous Galerkin methods on unstructured
grids with a WENO-type linear reconstruction and partial neighboring cells
Journal of Computational Physics, v228 (2009), pp..
Y. Xu and C.-W. Shu,
Local discontinuous Galerkin method for surface diffusion and Willmore flow of graphs
Journal of Scientific Computing, v40 (2009), pp.375-390.
I. Roy, J.-M. Qiu, C.-W. Shu and L.-Z. Fang,
A WENO algorithm for radiative transfer with resonant scattering
and the Wouthuysen-field coupling
New Astronomy, v14 (2009), pp.513-520.
I. Roy, W. Xu, J.-M. Qiu, C.-W. Shu and L.-Z. Fang,
Time evolution of Wouthuysen-field coupling
The Astrophysical Journal, v694 (2009), pp..
W. Chen, S.C. Wong, C.-W. Shu and P. Zhang,
Front tracking algorithm for the Lighthill-Whitham-Richards traffic
flow model with a piecewise quadratic, continuous, non-smooth, and
non-concave fundamental diagram
International Journal of Numerical Analysis and Modeling,
v6 (2009), pp.562-585.
Y. Lu, S.C. Wong, M. Zhang and C.-W. Shu,
The entropy solutions for the Lighthill-Whitham-Richards traffic flow model with a
discontinuous flow-density relationship
Transportation Science, v43 (2009), pp.511-530.
Y.-Y. Liu, C.-W. Shu and M.-P. Zhang,
On the positivity of linear weights in WENO approximations
Acta Mathematicae Applicatae Sinica,
English Series, v25 (2009), pp.503-538.
M. Zhang and C.-W. Shu,
Fourier analysis for discontinuous Galerkin and related methods
Chinese Science Bulletin, v54 (2009), pp..
Z. Xu, Y. Liu and C.-W. Shu,
Hierarchical reconstruction for spectral volume method on unstructured grids
Journal of Computational Physics, v228 (2009), pp..
W. Wang, C.-W. Shu, H.C. Yee and B. Sjogreen,
High-order well-balanced schemes and applications to non-equilibrium flow
Journal of Computational Physics, v228 (2009), pp..
S. Zhang, S. Jiang, Y.-T. Zhang and C.-W. Shu,
The mechanism of sound generation in the interaction between a
shock wave and two counter-rotating vortices
Physics of Fluids, v21 (2009), 076101.
Y. Cheng, I.M. Gamba, A. Majorana and C.-W. Shu,
A discontinuous Galerkin solver for Boltzmann-Poisson systems in nano devices
Computer Methods in Applied Mechanics and Engineering,
v198 (2009), pp..
Y. Xia, S.C. Wong and C.-W. Shu,
Dynamic continuum pedestrian flow model with memory effect
Physical Review E, v79 (2009), 066113.
S. Zhang, H. Zhang and C.-W. Shu,
Topological structure of shock induced vortex breakdown
Journal of Fluid Mechanics, v639 (2009), pp.343-372.
I. Roy, W. Xu, J.-M. Qiu, C.-W. Shu and L.-Z. Fang,
Wouthuysen-field coupling in 21 cm region around high-redshift sources
The Astrophysical Journal, v703 (2009), pp..
J. Cheng and C.-W. Shu,
High order schemes for CFD: a review
Chinese Journal of Computational Physics, v26 (2009), pp.633-655.
B. Dong and C.-W. Shu,
Analysis of a local discontinuous Galerkin method for linear
time-dependent fourth-order problems
SIAM Journal on Numerical Analysis, v47 (2009), pp..
W. Liu, J. Cheng and C.-W. Shu,
High order conservative Lagrangian schemes with Lax-Wendroff
type time discretization for the compressible Euler equations
Journal of Computational Physics, v228 (2009), pp..
Y. Liu, C.-W. Shu and Z. Xu,
Hierarchical reconstruction with up to second degree remainder
for solving nonlinear conservation laws
Nonlinearity, v22 (2009), pp..
Y. Jiang, T. Xiong, S.C. Wong, C.-W. Shu, M. Zhang, P. Zhang and W.H.K. Lam,
A reactive dynamic continuum user equilibrium model for bi-directional pedestrian
Acta Mathematica Scientia, v29B (2009), pp..
Y. Xu and C.-W. Shu,
Communications in Computational Physics, v7 (2010), pp.1-46.
Y. Xu and C.-W. Shu,
Dissipative numerical methods for the Hunter-Saxton equation
Journal of Computational Mathematics, v28 (2010), pp.606-620.
Y. Xia, Y. Xu and C.-W. Shu,
Local discontinuous Galerkin methods for the generalized Zakharov system
Journal of Computational Physics, v229 (2010), pp..
Y. Cheng and C.-W. Shu,
Superconvergence of discontinuous Galerkin and
local discontinuous Galerkin schemes for linear hyperbolic and
convection-diffusion equations in one space dimension
SIAM Journal on Numerical Analysis, v47 (2010), pp..
X. Zhang and C.-W. Shu,
On maximum-principle-satisfying high order schemes for scalar conservation laws
Journal of Computational Physics, v229 (2010), pp..
T. Xiong, M. Zhang, Y.-T. Zhang and C.-W. Shu,
Fast sweeping fifth order WENO scheme for static Hamilton-Jacobi
equations with accurate boundary treatment
Journal of Scientific Computing, v45 (2010), pp.514-536.
X. Zhang and C.-W. Shu,
A genuinely high order total variation diminishing scheme for
one-dimensional scalar conservation laws
SIAM Journal on Numerical Analysis, v48 (2010), pp.772-795.
Q. Zhang and C.-W. Shu,
Stability analysis and a priori error estimates of the third
order explicit Runge-Kutta discontinuous Galerkin Method for scalar
conservation laws
SIAM Journal on Numerical Analysis, v48 (2010), pp..
I. Roy, C.-W. Shu and L.-Z. Fang,
Resonant scattering and Ly$\alpha$ radiation emergent from neutral hydrogen halos
The Astrophysical Journal, v716 (2010), pp.604-614.
Y. Liu and C.-W. Shu,
Error analysis of the semi-discrete local
discontinuous Galerkin method for semiconductor device simulation models
Science China Mathematics, v53 (2010), pp..
J. Cheng and C.-W. Shu,
A cell-centered Lagrangian scheme with the
preservation of symmetry and conservation properties for
compressible fluid flows in two-dimensional cylindrical geometry
Journal of Computational Physics, v229 (2010), pp..
S. Tan and C.-W. Shu,
Inverse Lax-Wendroff procedure for numerical boundary conditions
of conservation laws
Journal of Computational Physics, v229 (2010), pp..
C. Wang and C.-W. Shu,
An interface treating technique for compressible multi-medium
flow with Runge-Kutta discontinuous Galerkin method
Journal of Computational Physics, v229 (2010), pp..
X. Zhang and C.-W. Shu,
On positivity-preserving high order discontinuous Galerkin schemes
for compressible Euler equations on rectangular meshes
Journal of Computational Physics, v229 (2010), pp..
Y. Xing, X. Zhang and C.-W. Shu,
Positivity-preserving high order well-balanced discontinuous
Galerkin methods for the shallow water equations
Advances in Water Resources, v33 (2010), pp..
W. Sun, S.C. Wong, P. Zhang and C.-W. Shu,
A shock-fitting algorithm for the Lighthill-Whitham-Richards
model on inhomogeneous highways
Transportmetrica, v7 (2011), pp.163-180.
R. Zhang, M. Zhang and C.-W. Shu,
On the order of accuracy and numerical performance
of two classes of finite volume WENO schemes
Communications in Computational Physics, v9 (2011), pp.807-827.
W. Wang, H.C. Yee, B. Sjogreen, T. Magin and C.-W. Shu,
Construction of low dissipative high-order well-balanced filter schemes
for non-equilibrium flows
Journal of Computational Physics, v230 (2011), pp..
W. Wang, J. Guzman and C.-W. Shu,
The multiscale discontinuous Galerkin method for solving a class of second
order elliptic problems with rough coefficients
International Journal of Numerical Analysis and Modeling,
v8 (2011), pp.28-47.
J.-M. Qiu and C.-W. Shu,
Conservative high order semi-Lagrangian finite difference
WENO methods for advection in incompressible flow
Journal of Computational Physics, v230 (2011), pp.863-889.
Y. Xing, C.-W. Shu and S. Noelle,
On the advantage of well-balanced schemes for moving-water
equilibria of the shallow water equations
Journal of Scientific Computing, v48 (2011), pp.339-349.
T. Xiong, M. Zhang, C.-W. Shu, S.C. Wong and P. Zhang,
High-order computational scheme for a dynamic continuum model for
bi-directional pedestrian flow
Computer Aided Civil and Infrastructure Engineering,
v26 (2011), pp.298-310.
Y. Xu and C.-W. Shu,
Local discontinuous Galerkin methods for the Degasperis-Procesi equation
Communications in Computational Physics, v10 (2011), pp.474-508.
W. Liu, L. Yuan and C.-W. Shu,
A conservative modification to the ghost fluid
method for compressible multiphase flows
Communications in Computational Physics, v10 (2011), pp.785-806.
S. Zhang, S. Jiang and C.-W. Shu,
Improvement of convergence to steady state
solutions of Euler equations with the WENO schemes
Journal of Scientific Computing, v47 (2011), pp.216-238.
Y. Cheng, I.M. Gamba, A. Majorana and C.-W. Shu,
A brief survey of the discontinuous Galerkin method for
the Boltzmann-Poisson equations
SEMA Journal, v54 (2011), pp.47-64.
X. Zhang and C.-W. Shu,
Positivity-preserving high order discontinuous Galerkin schemes
for compressible Euler equations with source terms
Journal of Computational Physics, v230 (2011), pp..
J.-M. Qiu and C.-W. Shu,
Conservative semi-Lagrangian finite difference WENO formulations with
applications to the Vlasov equation
Communications in Computational Physics, v10 (2011), pp.979-1000.
X.-T. Shi, J. Chen, W.-T. Bi, C.-W. Shu and Z.-S. She,
Numerical simulations of compressible mixing layers
with a discontinuous Galerkin method
Acta Mechanica Sinica, v27 (2011), pp.318-329.
O. Bokanowski, Y. Cheng and C.-W. Shu,
A discontinuous Galerkin solver for front propagation
SIAM Journal on Scientific Computing, v33 (2011), pp.923-938.
Y. Liu, C.-W. Shu and M. Zhang,
High order finite difference WENO schemes for nonlinear degenerate parabolic equations
SIAM Journal on Scientific Computing, v33 (2011), pp.939-965.
Y. Liu, C.-W. Shu, E. Tadmor and M. Zhang,
Central local discontinuous Galerkin methods
on overlapping cells for diffusion equations
ESAIM: Mathematical Modelling and Numerical Analysis (M2AN),
v45 (2011), pp..
X. Zhang and C.-W. Shu,
Maximum-principle-satisfying and positivity-preserving high-order
schemes for conservation laws: survey and new developments
Proceedings of the Royal Society A, v467 (2011), pp..
S. Tan and C.-W. Shu,
A high order moving boundary treatment for compressible inviscid flows
Journal of Computational Physics, v230 (2011), pp..
R. Zhang, M. Zhang and C.-W. Shu,
High order positivity-preserving finite volume WENO schemes for a
hierarchical size-structured population model
Journal of Computational and Applied Mathematics, v236 (2011), pp.937-949.
Z. Xu, Y. Liu, H. Du, G. Lin and C.-W. Shu,
Point-wise hierarchical reconstruction for discontinuous Galerkin and finite volume
methods for solving conservation laws
Journal of Computational Physics, v230 (2011), pp..
X. Zhong and C.-W. Shu,
Numerical resolution of discontinuous Galerkin methods for time
dependent wave equations
Computer Methods in Applied Mechanics and Engineering, v200 (2011),
Y. Xing and C.-W. Shu,
High-order finite volume WENO schemes for the shallow
water equations with dry states
Advances in Water Resources, v34 (2011), pp..
Y.-T. Zhang, S. Chen, F. Li, H. Zhao and C.-W. Shu,
Uniformly accurate discontinuous Galerkin fast sweeping methods
for Eikonal equations
SIAM Journal on Scientific Computing, v33 (2011), pp..
Y. Yang, I. Roy, C.-W. Shu and L.-Z. Fang,
Effect of dust on Ly$\alpha$ photon transfer in optically thick halo
The Astrophysical Journal, v739 (2011), 91.
B. Ayuso, J.A. Carrillo and C.-W. Shu,
Discontinuous Galerkin methods for the one-dimensional Vlasov-Poisson system
CITE>Kinetic and Related Models, v4 (2011), pp.955-989.
J.-M. Qiu and C.-W. Shu,
Positivity preserving semi-Lagrangian discontinuous Galerkin
formulation: theoretical analysis and application to the Vlasov-Poisson system
Journal of Computational Physics, v230 (2011), pp..
T. Xiong, P. Zhang, S.C. Wong, C.-W. Shu and M. Zhang,
A macroscopic approach to the lane formation phenomenon in pedestrian
counter flow
Chinese Physics Letters, v28 (2011), 108901.
Z. Xu, J. Xu and C.-W. Shu,
A high order adaptive finite element method for solving nonlinear
hyperbolic conservation laws
Journal of Computational Mathematics, v29 (2011), pp.491-500.
S. Zhang, S. Jiang, Q. Xu and C.-W. Shu,
Numerical study of shock vortex interaction with high order
finite difference WENO schemes
Computational Fluid Dynamics Journal, v18 (2011), pp.416-446.
C.-W. Shu,
Efficient algorithms for solving partial differential equations
with discontinuous solutions
Notices of the American Mathematical Society,
v59 (2012), pp.615-621.
Chinese translation in Mathematical Advances in Translation,
v33 (2015), pp.307-314.
J. Cheng and C.-W. Shu
Improvement on spherical symmetry in
two-dimensional cylindrical coordinates for a class of
control volume Lagrangian schemes
Communications in Computational Physics, v11 (2012),
X. Zhang, Y. Xia and C.-W. Shu,
Maximum-principle-satisfying and positivity-preserving
high order discontinuous Galerkin schemes for
conservation laws on triangular meshes
Journal of Scientific Computing, v50 (2012), pp.29-62.
W. Wang, C.-W. Shu, H.C. Yee and B. Sjogreen,
High order finite difference methods with subcell resolution for
advection equations with stiff source terms
Journal of Computational Physics, v231 (2012), pp.190-214.
X. Meng, C.-W. Shu and B. Wu,
Superconvergence of the local discontinuous Galerkin method
for linear fourth-order time-dependent problems in one space dimension
IMA Journal of Numerical Analysis, v32 (2012), pp..
C. Wang, X. Zhang, C.-W. Shu and J. Ning,
Robust high order discontinuous Galerkin schemes
for two-dimensional gaseous detonations
Journal of Computational Physics, v231 (2012), pp.653-665.
Y. Xu and C.-W. Shu,
Optimal error estimates of the semi-discrete local discontinuous
Galerkin methods for high order wave equations
SIAM Journal on Numerical Analysis, v50 (2012), pp.79-104.
X. Zhang and C.-W. Shu,
A minimum entropy principle of high order schemes
for gas dynamics equations
Numerische Mathematik, v121 (2012), pp.545-563.
X. Zhang and C.-W. Shu,
Positivity-preserving high order finite difference WENO schemes
for compressible Euler equations
Journal of Computational Physics, v231 (2012), pp..
S. Tan, C. Wang, C.-W. Shu and J. Ning,
Efficient implementation of high order inverse Lax-Wendroff
boundary treatment for conservation laws
Journal of Computational Physics, v231 (2012), pp..
X. Zhang, Y. Liu and C.-W. Shu,
Maximum-principle-satisfying high order finite volume
weighted essentially nonoscillatory schemes
for convection-diffusion equations
SIAM Journal on Scientific Computing, v34 (2012), pp.A627-A658.
J. Cheng, C.-W. Shu and Q. Zeng,
A conservative Lagrangian scheme for solving compressible
fluid flows with multiple internal energy equations
Communications in Computational Physics,
v12 (2012), pp..
T. Xiong, C.-W. Shu and M. Zhang,
WENO scheme with subcell resolution for computing nonconservative
Euler equations with applications to one-dimensional compressible
two-medium flows
Journal of Scientific Computing, v53 (2012), pp.222-247.
B. Ayuso de Dios, J.A. Carrillo and C.-W. Shu,
Discontinuous Galerkin methods for the multi-dimensional
Vlasov-Poisson problem
Mathematical Models and Methods in Applied Sciences,
v22 (2012), 1250042.
X. Meng, C.-W. Shu, Q. Zhang and B. Wu,
Superconvergence of discontinuous Galerkin method for scalar
nonlinear conservation laws in one space dimension
SIAM Journal on Numerical Analysis, v50 (2012), pp..
Y. Yang and C.-W. Shu,
Analysis of optimal superconvergence of discontinuous
Galerkin method for linear hyperbolic equations
SIAM Journal on Numerical Analysis, v50 (2012), pp..
C.-W. Shu,
On high order accurate weighted essentially non-oscillatory and
discontinuous Galerkin schemes for compressible turbulence simulations
Philosophical Transactions of the Royal Society A,
v371 (2013), .
X. Zhong and C.-W. Shu,
A simple weighted essentially nonoscillatory limiter for
Runge-Kutta discontinuous Galerkin methods
Journal of Computational Physics, v232 (2013), pp.397-415.
Y. Xing and C.-W. Shu,
High order well-balanced WENO scheme for the gas dynamics
equations under gravitational fields
Journal of Scientific Computing, v54 (2013), pp.645-662.
S.-H. Zhang, X.-G. Deng, M.-L Mao and C.-W. Shu,
Improvement of convergence to steady state solutions of Euler
equations with weighted compact nonlinear schemes
Acta Mathematicae Applicatae Sinica, English Series,
v29 (2013), pp.449-464.
Y. Zhang, X. Zhang and C.-W. Shu,
Maximum-principle-satisfying second order discontinuous Galerkin schemes
for convection-diffusion equations on triangular meshes
Journal of Computational Physics, v234 (2013), pp.295-316.
C. Wang, C.-W. Shu, W. Han and J. Ning,
High resolution WENO simulation of 3D detonation waves
Combustion and Flame, v160 (2013), pp.447-462.
T. Xiong, C.-W. Shu and M. Zhang,
A priori error estimates for semi-discrete discontinuous
Galerkin methods solving
nonlinear Hamilton-Jacobi equations with smooth solutions
International Journal of Numerical
Analysis and Modeling, v10 (2013), pp.154-177.
Y. Yang and C.-W. Shu,
Discontinuous Galerkin method for hyperbolic equations
involving $\delta$-singularities: negative-order norm error
estimates and applications
Numerische Mathematik, v124, (2013), pp.753-781.
Y. Jiang, C.-W. Shu and M. Zhang,
An alternative formulation of finite difference weighted
ENO schemes with Lax-Wendroff time discretization for conservation laws
SIAM Journal on Scientific Computing, v35 (2013), pp.A.
H.C. Yee, D.V. Kotov, W. Wang and C.-W. Shu,
Spurious behavior of shock-capturing methods by the fractional
step approach: problems
containing stiff source terms and discontinuities
Journal of Computational Physics, v241 (2013), pp.266-291.
X.Y. Hu, N.A. Adams and C.-W. Shu,
Positivity-preserving method for high-order conservative
schemes solving compressible Euler equations
Journal of Computational Physics, v242 (2013), pp.169-180.
Y. Xing, C.-S. Chou and C.-W. Shu,
Energy conserving local discontinuous Galerkin
methods for wave propagation problems
Inverse Problems and Imaging, v7 (2013), pp.967-986.
X. Liu, S. Zhang, H. Zhang and C.-W. Shu,
A new class of central compact schemes with
spectral-like resolution I: Linear schemes
Journal of Computational Physics, v248 (2013), pp.235-256.
J. Zhu, X. Zhong, C.-W. Shu and J.-X. Qiu,
Runge-Kutta discontinuous Galerkin method using a new
type of WENO limiters on unstructured meshes
Journal of Computational Physics, v248 (2013), pp.200-220.
S. Zhang, H. Li, X. Liu, H. Zhang and C.-W. Shu,
Classification and sound generation of two-dimensional
interaction of two Taylor vortices
Physics of Fluids, v25 (2013), 056103.
W. Hao, J.D. Hauenstein, C.-W. Shu, A.J. Sommese, Z. Xu and Y.-T. Zhang,
A homotopy method based on WENO schemes for solving steady state
problems of hyperbolic conservation laws
Journal of Computational Physics, v250 (2013), pp.332-346.
Y. Yang, I. Roy, C.-W. Shu and L.-Z. Fang,
Angular distribution of Ly$\alpha$ resonant photons emerging
from optically thick medium
The Astrophysical Journal, v772 (2013), 3.
Y. Yang, D. Wei and C.-W. Shu,
Discontinuous Galerkin method for Krause's consensus models and
pressureless Euler equations
Journal of Computational Physics, v252 (2013), pp.109-127.
J. Du, S.C. Wong, C.-W. Shu, T. Xiong, M. Zhang and K. Choi,
Revisiting Jiang's dynamic continuum model for urban cities
Transportation Research Part B, v56 (2013), pp.96-119.
J. Lu, C.-W. Shu and M. Zhang,
Stability analysis and a priori error estimate of explicit
Runge-Kutta discontinuous Galerkin methods for correlated random walk
with density-dependent turning rates
Science China Mathematics, v56 (2013), pp..
C.-W. Shu,
Bound-preserving high order accurate schemes
Notes of the Canadian Mathematical Society (CMS Notes),
v45 (2013), pp.24-25.
W. Zhu, L.-L. Feng, Y. Xia, C.-W. Shu, Q. Gu and L.-Z. Fang,
Turbulence in the intergalactic medium: solenoidal and
dilatational motions and the impact of numerical viscosity
The Astrophysical Journal, v777 (2013), 48.
C.-W. Shu,
A brief survey on discontinuous Galerkin methods in
computational fluid dynamics
Advances in Mechanics, v43 (2013), pp.541-554.
Y. Jiang, C.-W. Shu and M. Zhang,
Free-stream preserving finite difference schemes on curvilinear meshes
Methods and Applications of Analysis, v21 (2014), pp.1-30.
O. Bokanowski, Y. Cheng and C.-W. Shu,
A discontinuous Galerkin scheme for front propagation with obstacles
Numerische Mathematik, v126 (2014), pp.1-31.
Q. Zhang and C.-W. Shu,
Error estimates for the third order explicit Runge-Kutta
discontinuous Galerkin method for linear hyperbolic
equation in one-dimension with discontinuous initial data
Numerische Mathematik, v126 (2014), pp.703-740.
Z. Chen and C.-W. Shu,
Recovering exponential accuracy from collocation point
values of smooth functions with end-point singularities
conservative schemes
Journal of Computational and Applied Mathematics,
v265 (2014), pp.83-95.
J. Cheng and C.-W. Shu,
Positivity-preserving Lagrangian scheme for multi-material
compressible flow
Journal of Computational Physics, v257 (2014), pp.143-168.
Y. Zhang, W. Wang, J. Guzman and C.-W. Shu,
Multi-scale discontinuous Galerkin method for solving elliptic problems
with curvilinear unidirectional rough coefficients
Journal of Scientific Computing, v61 (2014), pp.42-60.
J. Niu, L. Zheng, Y. Yang and C.-W. Shu,
Chebyshev spectral method for unsteady axisymmetric mixed
convection heat transfer of power law fluid over a cylinder with
variable transport properties
International Journal of Numerical Analysis
and Modeling, v11 (2014), pp.525-540.
C.-S. Chou, C.-W. Shu and Y. Xing,
Optimal energy conserving local discontinuous Galerkin
methods for second-order wave equation in heterogeneous media
Journal of Computational Physics, v272 (2014), pp.88-107.
J. Cheng and C.-W. Shu,
Second order symmetry-preserving conservative
Lagrangian scheme for compressible Euler equations in
two-dimensional cylindrical coordinates
Journal of Computational Physics, v272 (2014), pp.245-265.
Y. Xing and C.-W. Shu,
A survey of high order schemes for the shallow water equations
Journal of Mathematical Study, v47 (2014), pp.221-249.
J. Du, C.-W. Shu and M. Zhang,
A simple weighted essentially non-oscillatory limiter for
the correction procedure via reconstruction (CPR) framework
Applied Numerical Mathematics, v95 (2015), pp.173-198.
F. Vilar and C.-W. Shu,
Development and stability analysis of the inverse Lax-Wendroff
boundary treatment for central compact schemes
ESAIM: Mathematical Modelling and Numerical Analysis
($M^{2}AN$), v49 (2015), pp.39-67.
W. Wang, C.-W. Shu, H.C. Yee, D.V. Kotov and B. Sj\"{o}green,
High order finite difference methods with subcell resolution for
stiff multispecies detonation capturing
Communications in Computational Physics,
v17 (2015), pp.317-336.
H. Wang, C.-W. Shu and Q. Zhang,
Stability and error estimates of local discontinuous
Galerkin methods with implicit-explicit time-marching for
advection-diffusion problems
SIAM Journal on Numerical Analysis, v53 (2015), pp.206-227.
X. Meng, C.-W. Shu and Y. Yang,
Superconvergence of discontinuous Galerkin methods for
time-dependent partial differential equations (in Chinese)
Scientia Sinica Mathematica, v45 (2015), pp..
J. Du, C.-W. Shu and M. Zhang,
A simple weighted essentially non-oscillatory limiter for
the correction procedure via reconstruction (CPR) framework on
unstructured meshes
Applied Numerical Mathematics, v90 (2015), pp.146-167.
X. Liu, S. Zhang, H. Zhang and C.-W. Shu,
A new class of central compact schemes with spectral-like
resolution II: Hybrid weighted nonlinear schemes
Journal of Computational Physics, v284 (2015), pp.133-154.
C. Wang and C.-W. Shu,
Progress on high-resolution numerical simulation of explosion
Chinese Science Bulletin (in Chinese), v60 (2015), pp.882-898.
J. Luo, C.-W. Shu and Q. Zhang,
A priori error estimates to smooth solutions of the third order
Runge-Kutta discontinuous
Galerkin method for symmetrizable systems of conservation laws
Mathematical Modelling and Numerical Analysis ($M^{2}AN$), v49 (2015), pp.991-1018.
L. Wu and C.-W. Shu,
Numerical solution of the viscous surface wave
with discontinuous Galerkin method
Mathematical Modelling and Numerical Analysis ($M^{2}AN$),
v49 (2015), pp..
Y. Jiang, C.-W. Shu and M. Zhang,
High order finite difference WENO schemes with
positivity-preserving limiter for correlated random walk
with density-dependent turning rates
Mathematical Models and Methods in Applied Sciences
($M^3 AS$), v25 (2015), pp..
Y. Yang and C.-W. Shu,
Analysis of sharp superconvergence of local discontinuous
Galerkin method for one-dimensional linear parabolic equations
Journal of Computational Mathematics, v33 (2015), pp.323-340.
Z. Chen and C.-W. Shu,
Recovering exponential accuracy in Fourier spectral methods
involving piecewise smooth functions with unbounded derivative singularities
Journal of Scientific Computing, v65 (2015), pp..
W. Cao, C.-W. Shu, Y. Yang and Z. Zhang,
Superconvergence of discontinuous Galerkin methods
for 2-D hyperbolic equations
SIAM Journal on Numerical Analysis, v53 (2015), pp..
C. Wang, X. Dong and C.-W. Shu,
Parallel adaptive mesh refinement method based on WENO
finite difference scheme for the simulation of multi-dimensional
detonation
Journal of Computational Physics, v298 (2015), pp.161-175.
J. Du, S.C. Wong, C.-W. Shu and M. Zhang,
Reformulating the Hoogendoorn-Bovy predictive dynamic
user-optimal model in continuum space with anisotropic condition
Transportation Research Part B, v79 (2015), pp.189-217.
X. Meng, C.-W. Shu and B. Wu,
Optimal error estimates for discontinuous Galerkin methods based
on upwind-biased fluxes for linear hyperbolic equations
Mathematics of Computation, v85 (2016), pp..
H. Wang, C.-W. Shu and Q. Zhang,
Stability analysis and error estimates of
local discontinuous Galerkin methods
with implicit-explicit time-marching
for nonlinear convection-diffusion problems
Applied Mathematics and Computation, v272 (2016), pp.237-258.
B. Dong, C.-W. Shu and W. Wang,
A new multiscale discontinuous Galerkin method for
the one-dimensional stationary Schr\"{o}dinger equation
Journal of Scientific Computing, v66 (2016), pp.321-345.
O. Bokanowski, Y. Cheng and C.-W. Shu,
Convergence of discontinuous Galerkin schemes for front
propagation with obstacles
Mathematics of Computation, v85 (2016), pp..
Y. Liu and C.-W. Shu,
Analysis of the local discontinuous Galerkin method for
the drift-diffusion model of semiconductor devices
Science China Mathematics, v59 (2016), pp.115-140.
J. Zhu, X. Zhong, C.-W. Shu and J.-X. Qiu,
Runge-Kutta discontinuous Galerkin method with a
simple and compact Hermite WENO limiter
Communications in Computational Physics,
v19 (2016), pp.944-969.
H. Wang, S. Wang, C.-W. Shu and Q. Zhang,
Local discontinuous Galerkin methods with implicit-explicit
time-marching for multi-dimensional convection-diffusion problems
Mathematical Modelling and Numerical Analysis ($M^{2}AN$),
v50 (2016), pp..
T. Li, C.-W. Shu and M. Zhang,
Stability analysis of the inverse Lax-Wendroff boundary
treatment for high order upwind-biased finite difference schemes
Journal of Computational and Applied Mathematics,
v299 (2016), pp.140-158.
L. Wu, Y.-T. Zhang, S. Zhang and C.-W. Shu,
High order fixed-point sweeping WENO methods for steady state
of hyperbolic conservation laws and its convergence study
Communications in Computational Physics,
v20 (2016), pp.835-869.
T. Qin, C.-W. Shu and Y. Yang,
Bound-preserving discontinuous Galerkin methods
for relativistic hydrodynamics
Journal of Computational Physics, v315 (2016), pp.323-347.
F. Vilar, C.-W. Shu and P.-H. Maire,
Positivity-preserving cell-centered Lagrangian schemes for
multi-material compressible flows: From first-order to high-orders.
Part I: The one-dimensional case
Journal of Computational Physics, v312 (2016), pp.385-415.
F. Vilar, C.-W. Shu and P.-H. Maire,
Positivity-preserving cell-centered Lagrangian schemes for
multi-material compressible flows: From first-order to high-orders.
Part II: The two-dimensional case
Journal of Computational Physics, v312 (2016), pp.416-442.
C.-W. Shu,
High order WENO and DG methods for time-dependent
convection-dominated PDEs: a brief survey of several
recent developments
Journal of Computational Physics, v316 (2016), pp.598-613.
J. Lu, J. Fang, S. Tan, C.-W. Shu and M. Zhang,
Inverse Lax-Wendroff procedure for numerical boundary
conditions of convection-diffusion equations
Journal of Computational Physics, v317 (2016), pp.276-300.
J. Du and C.-W. Shu,
A high order stable conservative method for solving hyperbolic
conservation laws on arbitrarily distributed point clouds
SIAM Journal on Scientific Computing,
v38 (2016), pp.A.
D. Yuan, J. Cheng and C.-W. Shu,
High order positivity-preserving discontinuous
Galerkin methods for radiative transfer equations
SIAM Journal on Scientific Computing, v38 (2016), pp.A.
C. Wang, J. Ding, C.-W. Shu and T. Li,
Three-dimensional high order large-scale numerical
investigation on the air explosion
Computers and Fluids, v137 (2016), pp.70-79.
D.S. Balsara, S. Garain and C.-W. Shu,
An efficient class of WENO schemes with adaptive order
Journal of Computational Physics, v326 (2016), pp.780-804.
Z. Sun and C.-W. Shu,
Stability analysis and error estimates of Lax-Wendroff
discontinuous Galerkin methods for linear conservation laws
ESAIM: Mathematical Modelling and Numerical
Analysis ($M^{2}AN$), v51 (2017), pp..
T. Li, C.-W. Shu and M. Zhang,
Stability analysis of the inverse
Lax-Wendroff boundary treatment for high order central
difference schemes for diffusion equations
Journal of Scientific Computing, v70 (2017), pp.576-607.
J. Huang and C.-W. Shu,
Error estimates to smooth solutions of semi-discrete
discontinuous Galerkin methods with quadrature rules for
scalar conservation laws
Numerical Methods for Partial Differential Equations,
v33 (2017), pp.467-488.
J. Zhu, X. Zhong, C.-W. Shu and J. Qiu,
Runge-Kutta discontinuous Galerkin method with a simple
and compact Hermite WENO limiter on unstructured meshes
Communications in Computational Physics, v21 (2017), pp.623-649.
J. Guzman, C.-W. Shu and F.A. Sequeira,
H(div) conforming and DG methods for incompressible Euler's
IMA Journal of Numerical Analysis, v37 (2017), pp..
H. Shen, C.-Y. Wen, M. Parsani and C.-W. Shu,
Maximum-principle-satisfying space-time conservation
element and solution element scheme applied to compressible
multifluids
Journal of Computational Physics, v330 (2017), pp.668-692.
Z. Sun and C.-W. Shu,
Stability of the fourth order Runge-Kutta method for
time-dependent partial differential equations
Annals of Mathematical Sciences and Applications,
v2 (2017), pp.255-284.
J. Huang and C.-W. Shu,
A second-order asymptotic-preserving and positive-preserving
discontinuous Galerkin scheme for the Kerr-Debye model
Mathematical Models and Methods in Applied
Sciences, v27 (2017), pp.549–579.
X.H. Li, C.-W. Shu and Y. Yang,
Journal of Scientific Computing, to appear.
G. Fu and C.-W. Shu,
Analysis of an embedded discontinuous Galerkin method
with implicit-explicit time-marching for convection-diffusion
International Journal of Numerical
Analysis and Modeling, v14 (2017), pp.477-499.
C.Y. Lam and C.-W. Shu,
A phase-based interior penalty discontinuous Galerkin method
for the Helmholtz equation with spatially varying wavenumber
Computer Methods in Applied Mechanics and
Engineering, v318 (2017), pp.456-473.
F. Zheng, C.-W. Shu and J. Qiu,
Finite difference Hermite WENO schemes for
the Hamilton-Jacobi equations
Journal of Computational Physics, v337 (2017), pp.27-41.
J. Li, C. Shi and C.-W. Shu,
Optimal non-dissipative discontinuous Galerkin methods for
Maxwell's equations in Drude metamaterials
Computers and Mathematics with Applications, v73 (2017), pp..
Y. Liu, Y. Cheng and C.-W. Shu,
Journal of Scientific Computing, to appear.
H. Wang, Q. Zhang and C.-W. Shu,
Stability analysis and error estimates of local discontinuous
Galerkin methods with implicit-explicit time-marching for the
time-dependent fourth order PDEs
ESAIM: Mathematical Modelling and Numerical
Analysis ($M^{2}AN$), to appear.
Q. Liu, C.-W. Shu and M. Zhang,
Discontinuous Galerkin methods for weakly coupled hyperbolic
multi-domain problems
SIAM Journal on Scientific Computing,
v321 (2017), pp.209-234.
J. Morales-Escalante, I.M. Gamba, Y. Cheng, A. Majorana,
C.-W. Shu and J. Chelikowsky,
Discontinuous Galerkin deterministic solvers for a
Boltzmann-Poisson model of hot electron transport byaveraged empirical pseudopotential band structures
Computer Methods in Applied Mechanics and Engineering,
v321 (2017), pp.209-234.
W. Cao, C.-W. Shu and Z. Zhang,
ESAIM: Mathematical Modelling and Numerical
Analysis ($M^{2}AN$), to appear.
J. Du and C.-W. Shu,
International Journal of Numerical
Analysis and Modeling, to appear.
T. Chen and C.-W. Shu,
Entropy stable high order discontinuous Galerkin
methods with suitable quadrature rules
for hyperbolic conservation laws
Journal of Computational Physics, v345 (2017), pp.427-461.
C. Shi and C.-W. Shu,
Computers and Fluids, to appear.
H. Wang, Y. Liu, Q. Zhang and C.-W. Shu,
Mathematics of Computation, to appear.
G. Fu and C.-W. Shu,
A new trouble-cell indicator for discontinuous Galerkin
methods for hyperbolic conservation laws
Journal of Computational Physics, v347 (2017),
pp.305-327.
H. Song and C.-W. Shu,
Journal of Scientific Computing, to appear.
J. Zhu and C.-W. Shu,
Numerical study on the convergence to steady state solutions of
a new class of high order WENO schemes
Journal of Computational Physics, v349 (2017), pp.80-96.
D. Ling, J. Cheng and C.-W. Shu,
Positivity-preserving and symmetry-preserving Lagrangian
schemes for compressible Euler equations in cylindrical coordinates,
Computers and Fluids, v157 (2017), pp.112-130.
Z. Sun, J.A. Carrillo and C.-W. Shu,
A discontinuous Galerkin method for nonlinear parabolic
equations and gradient flow problems with interaction
potentials
Journal of Computational Physics, v352 (2018), pp.76-104.
T. Qin and C.-W. Shu,
SIAM Journal on Scientific Computing, to appear.
B. Cockburn and C.-W. Shu,
in Hyperbolic Problems: Theory, Numerics,
Applications, T.Y. Hou and E. Tadmor, editors, Springer-Verlag,