Papers (54):

Y. Xu, and Q. Zhang,
A note on Stabilty analysis of two dimensional RungeKutta discontinuous Galerkin method,
Communications on Applied Mathematics and Computation, online 
S. Q. Zheng, M. Tang, Q. Zhang and T. Xiong,
High order conservative LDGIMEX methods for the degenerate nonlinear nonequilibrium radiation diffusion problems,
J. Computational Physics, 503(2024), 29pp, paper no. 112838. 
Y. Tan, Q. Zhang and J. Zhu,
The fifthorder finite volume distinct unequalsized WENO schemes for extreme problems of Euler equations,
J. Scientific Computing, 99:27 (2024), 27pp. 
H. J. Wang, F. Y. Li, C.W. Shu and Q. Zhang,
Uniform stability for local discontinuous Galerkin methods with implicitexplicit RungeKutta time discretizations for linear convectiondiffusion equation,
Mathematica Computation, 92:344 (2023), 24752513 
H. J. Wang, X. B. Shi and Q. Zhang,
Stability and error estimates of local discontinuous Galerkin methods with implicitexplicit backward difference formulas up to fifth order for convectiondiffusion equation,
J. Scientific Computing, 96:2 (2023), 25pp, articel 37 
Z. H. Wang, Z. Gao, H. Y. Wang, Q. Zhang and H. Q. Zhu,
Three indication variables and their performance for the troublecell indictor using Kmeans clustering,
Advances in Applied Mathematics and Mechanics, 15:2 (2023), 522544 
H. Q. Zhu, Z. H. Wang, H.Y. Wang, Q. Zhang and Z. Gao,
Troublecell indicator using Kmeans clustering with unifed parameter,
J. Scientific Computing, 93:21 (2022), 29pp, article 21 
J. Q. Ai, Y. Xu, C.W. Shu and Q. Zhang,
L2 error estimate to smooth solution of high order RKDG method for scalar nonlinear conservation laws with and without sonic points,
SIAM J. Numerical Analysis, 60:4 (2022), 17411773 
Y. Xu, D. Zhao and Q. Zhang,
Local error estimates for RungeKutta discontinuous Galerkin methods with upwindbiased numerical fluxes for a linear hyperbolic equations in onedimension with discontinuous initial data,
J. Scientific Computing, 91:11 (2022), 30pp, article 11 
Y. Xu, and Q. Zhang,
Superconvergence analysis of the RungeKutta discontinuous Galerkin method with upwindbiased numerical flux for two dimensional linear hyperbolic equation,
Communications on Applied Mathematics and Computation, 4:1 (2022), 271292 
H.J. Wang, and Q. Zhang,
The direct discontinuous Galerkin methods with implicitexplicit RungeKutta time marching for linear convection diffusion problems,
Communications on Applied Mathematics and Computation, 4:1 (2022), 319352 
Y. Xu, C.W. Shu, and Q. Zhang,
Error estimate of the fourth order RungeKutta discontinuous Galerkin methods for linear hyperbolic equations,
SIAM J. Numerical Analysis, 58:5 (2020), 28852914 
Y. Xu, X. Meng, C.W. Shu, and Q. Zhang,
Superconvergence analysis of the RungeKutta discontinuous Galerkin methods for a linear hyperbolic equation,
J. Scientific Computing, 84:23 (2020), 40pp, article 23 
J. Li, D.Z. Zhang, X. Meng, B.Y. Wu, and Q. Zhang,
Discontinuous Galerkin methods for nonlinear scalar conservation laws: generalized local LaxFredrichs numerical fluxes,
SIAM J. Numerical Analysis, 58:1 (2020), 120 
H.J. Wang, Q. Zhang, S.P. Wang and C.W. Shu,
Local discontinuous Galerkin methods with explicitimplicitnull time discretizations for solving nonlinear diffusion problems,
Chinese Science Mathematics, 63:1 (2020), 183204 
H.J. Wang, Q. Zhang, and C.W. Shu,
Implicitexplicit local discontinuous Galerkin methods with generalized alternating numerical fluxes for convectiondiffusion problems,
J. Scientific Computing, 81(2019), 20802114 
Y. Xu, Q. Zhang, C.W. Shu, and H.J. Wang,
The L2norm stability analysis of RungeKutta discontinuous Galerkin methods for linear hyperbolic equations,
SIAM J. Numerical Analysis, 57:4 (2019), 15741601 
D. Zhao, and Q. Zhang,
Local discontinuous Galerkin methods with generalized alternating numerical fluxes for twodimensional linear Sobolev equation,
J. Scientific Computing, 78:3 (2019), 16601690 
H.J. Wang, J.J. Zheng, F. Yu, H. Guo, and Q. Zhang,
Local discontinuous Galerkin method with implicitexplicit time marching for incompressible miscible displacement problem in porous media,
J. Scientific Computing, 78:1 (2019), 128 
H.J. Wang, Y.X. Liu, Q. Zhang, and C.W. Shu,
Local discontinuous Galerkin methods with implicitexplicit timemarching for timedependent incompressible fluid flow,
Mathematica Computation, 88:315 (2019), 91121 
Y. Cheng, Q. Zhang, and H.J. Wang,
Local analysis of the local discontinuous Galerkin method with the generalized alternating numerical fluxes for twodimensional singularity perturbed problem,
I. J. Numerical Analysis and Modeling, 15:6 (2018), 785810 
H.J. Wang, Q. Zhang, and C.W. Shu,
Third order implicitexplicit RungeKutta local discontinuous Galerkin methods with suitable boundary treatment for convectiondiffusion problems with Dirichlet boundary conditions,
J. Computational and Applied Mathematics, 342 (2018), 164179 
H.J. Wang, Q. Zhang, and C.W. Shu,
Stability analysis and error estimates of local discontinuous Galerkin methods with implicitexplicit timemarching for the timedependent fourth order PDEs,
ESAIM: Mathematical Modelling and Numerical Analysis, 51 (2017), 19311955 
Y. Cheng, and Q. Zhang,
Local analysis of local discontinuous Galerkin method with generalized alternating numerical flux for onedimensional singularity perturbed problem,
J. Scientific Computing, 72 (2017), 792819 
Y. Cheng, and Q. Zhang,
Local analysis of the fully discrete local discontinuous Galerkin method for the timedependent singularly perturbed problem,
J. Computational Mathematic, 35:3 (2017), 265288 
Y. Cheng, X. Meng, and Q. Zhang,
Application of generalized GaussRadau projections for the local discontinuous Galerkin method for linear convectiondiffusion equations,
Mathematica Computation, 305( 2017), 12331267. 
H.J. Wang, S.P. Wang, Q. Zhang, and C.W. Shu,
Local discontinuous Galerkin methods with implicitexplicit timemarching for multidimensional convection diffusion problems,
ESAIM: Mathematical Modelling and Numerical Analysis, 50 (2016), 10831105 
H.J. Wang, C.W. Shu, and Q. Zhang,
Stability analysis and error estimates of local discontinuous Galerkin methods with implicitexplicit timemarching for nonlinear convection diffusion problems,
Applied Mathematics and Computation, 272:2 (2016), 237258 
J. Luo, C.W. Shu, and Q. Zhang,
A priori estimates to smooth solutions of the third order RungeKutta discontinuous Galerkin method for symmetrizable system of conservation laws,
ESAIM: Mathematical Modelling and Numerical Analysis, 49 (2015), 9911018 
H.J. Wang, C.W. Shu, and Q. Zhang,
Stability and error estimates of local discontinuous Galerkin methods with implicitexplicit timemarching for convection diffusion problems,
SIAM J. Numerical Analysis, 53:1 (2015), 206227 
Y. Cheng, F. Zhang, and Q. Zhang,
Local analysis of local discontinuous Galerkin method for the timedependent singularity perturbed problem,
J. Scientific Computing, 63 (2015), 452477 
Q. Zhang, and C.W. Shu,
Error estimate for the third order explicit RungeKutta discontinuous Galerkin method for a linear hyperbolic equation with discontinuous initial solution,
Numerische Mathematik, 126 (2014), 703740 
Y.H. Xue, H.Y. Duan, and Q. Zhang,
A new and simple improvement of the Elementallocal L2projection Continuous finite element method,
Applied Mathematics and Computation, 228 (2014), 170183. 
H.J. Wang, and Q. Zhang,
Error estimate on a fully discrete local discontinuous Galerkin method for linear convectiondiffusion problem,
J. Computational Mathematics, 31:3(2013), 283307 
X. Meng, C.W. Shu, Q. Zhang, and B.Y. Wu,
Superconvergence of discontinuous Galerkin method for scalar nonlinear conservation laws in one dimension,
SIAM J. Numerical Analysis, 50:5(2012), 23262356 
Q. Zhang, and F.Z. Gao,
Explicit RungeKutta local discontinuous Galerkin method for convection dominated Sobolev equation,
J. Scientific Computing, 51:1(2012), 107134 
Q. Zhang,
Third order explicit RungeKutta discontinuous Galerkin method for linear conservation law with inflow boundary condition,
J. Scientific Computing, 46:2(2011), 294313 
Z. Qian, and Q. Zhang,
Differentialdifference regularization for a 2d inverse heat conduction problem,
INVERSE Problem 26(2010). 095015(16pp). DOI. 10.1088/02665611/26/9/095015 
Q. Zhang, and C.W. Shu,
Stability analysis and a priori error estimate to the third order explicit RungeKutta discontinuous Galerkin method for scalar conservation laws,
SIAM. J. Numerical Analysis, 48:3(2010), 10381063 
W. Yuan, Y.P. Zhao, Q. Zhang and Y. Sun,
Protein adsorptiondependent electrokinetic pore flow: modeling of ionexchange electrochromatography with an oscillatory transverse electric field,
ELECTROPHORESIS, 31(2010), 944951(*) 
F.Z. Gao, J.X. Qiu, and Q. Zhang,
Local discontinuous Galerkin finite element method and error estimates for one class of Sobolev equation,
J. Scientific Computing, 41:3(2009), 436460 
Q. Zhang, and Z.L. Wu,
Numerical simulation for porous medium equation by local discontinuous Galerkin finite element method,
J. Scientific Computing, 38:2(2009), 127148 
Q. Zhang,
Adaptive discontinuous Galerkin finite element methods for two dimensional convectiondiffusion equation,
J. Numerical Methods and Computer Applications (Chinese), 29:1(2008), 5664 
Q. Zhang, and C.W. Shu,
Error estimates to smooth solution of RungeKutta discontinuous Galerkin methods for symmetrizable system of conservation laws,
SIAM. J. Numerical Analysis, 44:4(2006), 17021720 
Q. Zhang, and C.W. Shu,
Error estimates to smooth solution of RungeKutta discontinuous Galerkin methods for scalar conservation laws,
SIAM. J. Numerical Analysis, 42:2(2004), 641666 
Q. Zhang, M.P. Zhang, G.D. Jin and D.Y. Liu,
Modeling, numerical method, and simulation for particlefluid twophase flow problems,
Computers and Mathematics with Applications, 47(2004), 14371462 
Q. Zhang,
Splitting scheme of finitedifference streamlinediffusion method for linear convection diffusion equation,
Communication on Applied Analysis, 8:2(2004), 185203 
Q. Zhang,
Finite difference streamline diffusion method for incompressible Navier Stokes equation,
Mathematica Numerical Sinica (Chinese), 25:3(2003), 311320 
Q. Zhang,
FDSD method and its error estimates for twophase incompressible miscible flow in porous media,
Acta Mathematicae Applicatae Sinica (Chinese), 26:2(2003), 318327 
Q. Zhang,
Local stability analysis of finitedifference streamline diffusion method,
Mathematica Applicata (Chinese), 15:2(2002), 6267 
Q. Zhang,
Finitedifference streamline diffusion method for linear convectiondiffusion equation,
Mathematica Applicata (Chinese), 12:3(1999), 101108 
Q. Zhang, and C. Sun,
Predictcorrection FDSD method for one class of nonlinear convection diffusion equation,
Acta Mathematicae Applicatae Sinica (Chinese), 21:3(1999), 363374;
translation in Chinese J. Numer. Math. Appl. (English), 21:4 (1999), 7992 
Q. Zhang, and C. Sun,
Finitedifference streamlinediffusion method for nonlinear convectiondiffusion equation,
Acta Mathematicae Applicatae Sinica (Chinese), 20:2(1998), 213224;
translation in Chinese J. Numer. Math. Appl. (English), 20:3 (1998), 6174 
Q. Zhang, and H.M. Tang,
Characteristic finite difference method for nonlinear convection diffusion equation with third boundary condition,
Acta Scientiarum Naturalium Universititatis Nankaiensis (Chinese), 29:1(1996), 1423(*)
Books (1):

J.X. Qiu, and Q. Zhang,
Stability, error estimate and limiters of discontinuous Galerkin methods, in: Handbook of numerical methods for hyperbolic problems,
Handbook of Numerical Analysis,17 (2016), 147171, Elsevier/NorthHolland, Amsterdam
Preprints (4):

H. J. Wang, L. L. Jiang, Q. Zhang, Y. Xu, and X. B. Shi,
Ultraweak discontinuous Galerkin method with IMEXBDF time marching for two dimensional convectiondiffusion problems,
submitted to CAMWA 
H. J. Wang, Q. Tao, C.W. Shu, and Q. Zhang,
Analysis og local discontinuous Galerkin methods with implicitexplicit time marching for linearized KdV equations,
submitted to SINUM 
Y. Xu, C.W. Shu and Q. Zhang,
Stabilty analysis and error estimate of the explicit single step time marching discontinuous Galerkin method with stagedependent numerical flux parameters for a linear hyperbolic equation in one dimension,
submitted to JSC 
H. Y. Wang, Z. Gao, H. J. Wang, Q. Zhang and H. Q. Zhu,
Troubledcell indicators using Kmeans clustering for RKDG methods on triangular meshes and hadaptive rectangular meshes,
accepted by Advances in Applied Mathematics and Mechanics