Publications

Papers (54):

  • Y. Xu, and Q. Zhang,
    A note on Stabilty analysis of two dimensional Runge-Kutta discontinuous Galerkin method,
    Communications on Applied Mathematics and Computation, online
  • S. Q. Zheng, M. Tang, Q. Zhang and T. Xiong,
    High order conservative LDG-IMEX methods for the degenerate nonlinear non-equilibrium radiation diffusion problems,
    J. Computational Physics, 503(2024), 29pp, paper no. 112838.
  • Y. Tan, Q. Zhang and J. Zhu,
    The fifth-order finite volume distinct unequal-sized 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 implicit-explicit Runge-Kutta time discretizations for linear convection-diffusion equation,
    Mathematica Computation, 92:344 (2023), 2475-2513
  • 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 convection-diffusion 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 trouble-cell indictor using K-means clustering,
    Advances in Applied Mathematics and Mechanics, 15:2 (2023), 522-544
  • H. Q. Zhu, Z. H. Wang, H.Y. Wang, Q. Zhang and Z. Gao,
    Trouble-cell indicator using K-means 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), 1741-1773
  • Y. Xu, D. Zhao and Q. Zhang,
    Local error estimates for Runge-Kutta discontinuous Galerkin methods with upwind-biased numerical fluxes for a linear hyperbolic equations in one-dimension with discontinuous initial data,
    J. Scientific Computing, 91:11 (2022), 30pp, article 11
  • Y. Xu, and Q. Zhang,
    Superconvergence analysis of the Runge-Kutta discontinuous Galerkin method with upwind-biased numerical flux for two dimensional linear hyperbolic equation,
    Communications on Applied Mathematics and Computation, 4:1 (2022), 271-292
  • H.J. Wang, and Q. Zhang,
    The direct discontinuous Galerkin methods with implicit-explicit Runge-Kutta time marching for linear convection diffusion problems,
    Communications on Applied Mathematics and Computation, 4:1 (2022), 319-352
  • Y. Xu, C.-W. Shu, and Q. Zhang,
    Error estimate of the fourth order Runge-Kutta discontinuous Galerkin methods for linear hyperbolic equations,
    SIAM J. Numerical Analysis, 58:5 (2020), 2885-2914
  • Y. Xu, X. Meng, C.-W. Shu, and Q. Zhang,
    Superconvergence analysis of the Runge-Kutta 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 Lax-Fredrichs numerical fluxes,
    SIAM J. Numerical Analysis, 58:1 (2020), 1-20
  • H.J. Wang, Q. Zhang, S.P. Wang and C.-W. Shu,
    Local discontinuous Galerkin methods with explicit-implicit-null time discretizations for solving nonlinear diffusion problems,
    Chinese Science Mathematics, 63:1 (2020), 183-204
  • H.J. Wang, Q. Zhang, and C.-W. Shu,
    Implicit-explicit local discontinuous Galerkin methods with generalized alternating numerical fluxes for convection-diffusion problems,
    J. Scientific Computing, 81(2019), 2080-2114
  • Y. Xu, Q. Zhang, C.-W. Shu, and H.J. Wang,
    The L2-norm stability analysis of Runge-Kutta discontinuous Galerkin methods for linear hyperbolic equations,
    SIAM J. Numerical Analysis, 57:4 (2019), 1574-1601
  • D. Zhao, and Q. Zhang,
    Local discontinuous Galerkin methods with generalized alternating numerical fluxes for two-dimensional linear Sobolev equation,
    J. Scientific Computing, 78:3 (2019), 1660-1690
  • H.J. Wang, J.J. Zheng, F. Yu, H. Guo, and Q. Zhang,
    Local discontinuous Galerkin method with implicit-explicit time marching for incompressible miscible displacement problem in porous media,
    J. Scientific Computing, 78:1 (2019), 1-28
  • H.J. Wang, Y.X. Liu, Q. Zhang, and C.-W. Shu,
    Local discontinuous Galerkin methods with implicit-explicit time-marching for time-dependent incompressible fluid flow,
    Mathematica Computation, 88:315 (2019), 91-121
  • Y. Cheng, Q. Zhang, and H.J. Wang,
    Local analysis of the local discontinuous Galerkin method with the generalized alternating numerical fluxes for two-dimensional singularity perturbed problem,
    I. J. Numerical Analysis and Modeling, 15:6 (2018), 785-810
  • H.J. Wang, Q. Zhang, and C.-W. Shu,
    Third order implicit-explicit Runge-Kutta local discontinuous Galerkin methods with suitable boundary treatment for convection-diffusion problems with Dirichlet boundary conditions,
    J. Computational and Applied Mathematics, 342 (2018), 164-179
  • H.J. 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, 51 (2017), 1931-1955
  • Y. Cheng, and Q. Zhang,
    Local analysis of local discontinuous Galerkin method with generalized alternating numerical flux for one-dimensional singularity perturbed problem,
    J. Scientific Computing, 72 (2017), 792-819
  • Y. Cheng, and Q. Zhang,
    Local analysis of the fully discrete local discontinuous Galerkin method for the time-dependent singularly perturbed problem,
    J. Computational Mathematic, 35:3 (2017), 265-288
  • Y. Cheng, X. Meng, and Q. Zhang,
    Application of generalized Gauss-Radau projections for the local discontinuous Galerkin method for linear convection-diffusion equations,
    Mathematica Computation, 305( 2017), 1233-1267.
  • H.J. Wang, S.P. Wang, Q. Zhang, and C.-W. Shu,
    Local discontinuous Galerkin methods with implicit-explicit time-marching for multi-dimensional convection diffusion problems,
    ESAIM: Mathematical Modelling and Numerical Analysis, 50 (2016), 1083-1105
  • H.J. 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, 272:2 (2016), 237-258
  • J. Luo, C.-W. Shu, and Q. Zhang,
    A priori estimates to smooth solutions of the third order Runge-Kutta discontinuous Galerkin method for symmetrizable system of conservation laws,
    ESAIM: Mathematical Modelling and Numerical Analysis, 49 (2015), 991-1018
  • H.J. Wang, C.-W. Shu, and Q. Zhang,
    Stability and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for convection diffusion problems,
    SIAM J. Numerical Analysis, 53:1 (2015), 206-227
  • Y. Cheng, F. Zhang, and Q. Zhang,
    Local analysis of local discontinuous Galerkin method for the time-dependent singularity perturbed problem,
    J. Scientific Computing, 63 (2015), 452-477
  • Q. Zhang, and C.-W. Shu,
    Error estimate for the third order explicit Runge-Kutta discontinuous Galerkin method for a linear hyperbolic equation with discontinuous initial solution,
    Numerische Mathematik, 126 (2014), 703-740
  • Y.H. Xue, H.Y. Duan, and Q. Zhang,
    A new and simple improvement of the Elemental-local L2-projection Continuous finite element method,
    Applied Mathematics and Computation, 228 (2014), 170-183.
  • H.J. Wang, and Q. Zhang,
    Error estimate on a fully discrete local discontinuous Galerkin method for linear convection-diffusion problem,
    J. Computational Mathematics, 31:3(2013), 283-307
  • 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), 2326-2356
  • Q. Zhang, and F.Z. Gao,
    Explicit Runge-Kutta local discontinuous Galerkin method for convection dominated Sobolev equation,
    J. Scientific Computing, 51:1(2012), 107-134
  • Q. Zhang,
    Third order explicit Runge-Kutta discontinuous Galerkin method for linear conservation law with inflow boundary condition,
    J. Scientific Computing, 46:2(2011), 294-313
  • Z. Qian, and Q. Zhang,
    Differential-difference regularization for a 2d inverse heat conduction problem,
    INVERSE Problem 26(2010). 095015(16pp). DOI. 10.1088/0266-5611/26/9/095015
  • Q. Zhang, and C.-W. Shu,
    Stability analysis and a priori error estimate to the third order explicit Runge-Kutta discontinuous Galerkin method for scalar conservation laws,
    SIAM. J. Numerical Analysis, 48:3(2010), 1038-1063
  • W. Yuan, Y.P. Zhao, Q. Zhang and Y. Sun,
    Protein adsorption-dependent electro-kinetic pore flow: modeling of ion-exchange electro-chromatography with an oscillatory transverse electric field,
    ELECTROPHORESIS, 31(2010), 944-951(*)
  • 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), 436-460
  • 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), 127-148
  • Q. Zhang,
    Adaptive discontinuous Galerkin finite element methods for two dimensional convection-diffusion equation,
    J. Numerical Methods and Computer Applications (Chinese), 29:1(2008), 56-64
  • Q. Zhang, and C.-W. Shu,
    Error estimates to smooth solution of Runge-Kutta discontinuous Galerkin methods for symmetrizable system of conservation laws,
    SIAM. J. Numerical Analysis, 44:4(2006), 1702-1720
  • Q. Zhang, and C.-W. Shu,
    Error estimates to smooth solution of Runge-Kutta discontinuous Galerkin methods for scalar conservation laws,
    SIAM. J. Numerical Analysis, 42:2(2004), 641-666
  • Q. Zhang, M.P. Zhang, G.D. Jin and D.Y. Liu,
    Modeling, numerical method, and simulation for particle-fluid two-phase flow problems,
    Computers and Mathematics with Applications, 47(2004), 1437-1462
  • Q. Zhang,
    Splitting scheme of finite-difference streamline-diffusion method for linear convection diffusion equation,
    Communication on Applied Analysis, 8:2(2004), 185-203
  • Q. Zhang,
    Finite difference streamline diffusion method for incompressible Navier Stokes equation,
    Mathematica Numerical Sinica (Chinese), 25:3(2003), 311-320
  • Q. Zhang,
    FDSD method and its error estimates for two-phase incompressible miscible flow in porous media,
    Acta Mathematicae Applicatae Sinica (Chinese), 26:2(2003), 318-327
  • Q. Zhang,
    Local stability analysis of finite-difference streamline diffusion method,
    Mathematica Applicata (Chinese), 15:2(2002), 62-67
  • Q. Zhang,
    Finite-difference streamline diffusion method for linear convection-diffusion equation,
    Mathematica Applicata (Chinese), 12:3(1999), 101-108
  • Q. Zhang, and C. Sun,
    Predict-correction FDSD method for one class of nonlinear convection diffusion equation,
    Acta Mathematicae Applicatae Sinica (Chinese), 21:3(1999), 363-374;
    translation in Chinese J. Numer. Math. Appl. (English), 21:4 (1999), 79-92
  • Q. Zhang, and C. Sun,
    Finite-difference streamline-diffusion method for nonlinear convection-diffusion equation,
    Acta Mathematicae Applicatae Sinica (Chinese), 20:2(1998), 213-224;
    translation in Chinese J. Numer. Math. Appl. (English), 20:3 (1998), 61-74
  • 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), 14-23(*)

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), 147-171, Elsevier/North-Holland, Amsterdam

Preprints (4):

  • H. J. Wang, L. L. Jiang, Q. Zhang, Y. Xu, and X. B. Shi,
    Ultra-weak discontinuous Galerkin method with IMEX-BDF time marching for two dimensional convection-diffusion problems,
    submitted to CAMWA
  • H. J. Wang, Q. Tao, C-.W. Shu, and Q. Zhang,
    Analysis og local discontinuous Galerkin methods with implicit-explicit 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 stage-dependent 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,
    Troubled-cell indicators using K-means clustering for RKDG methods on triangular meshes and h-adaptive rectangular meshes,
    accepted by Advances in Applied Mathematics and Mechanics