Nanjing University, China

Papers (57):

• 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,
  Computers and Mathematics with Applications, 176 (2024), 77-90
• H. J. Wang, Q. Tao, C-.W. Shu, and Q. Zhang,
  Analysis of local discontinuous Galerkin methods with implicit-explicit time marching for linearized KdV equations,
  SIAM. J. Numerical Analysis, 62:5 (2024), 2222-2248
• 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,
  J. Scientific Computing, 100:3 (2024), 47pp, page no. 64
• 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,
  A new positivity-preserving technique for high-order schemes to solve extreme problems of Euler equations on structured meshes,
  J. Scientific Computing, 99:1 (2024), 29pp, page no. 27
• 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, page no. 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, page no. 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, 91:1 (2022), 30pp, page no. 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, page no. 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
  Note: A correction to the proof of Lemma 2.3 is given in 101:59 (2024)
• 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):

• C. Y. Du, D. Zhao, and Q. Zhang,
  Error estimate of high order Runge-Kutta local discontinuous Galerkin method for nonlinear convection-dominated Sobolev equation,
  submitted to JCAM
• Y. Xu, X. Meng, C.-W. Shu, and Q. Zhang,
  Optimal error estimate of a discontinuous Galerkin method for one-dimensional linear hyperbolic equation with degenerate points moving along space-time curves,
  submitted to JSC
• H. J. Wang, Q. Zhang, C-.W. Shu, and Q. Tao,
  Stability and error analysis of a third order fully discrete local discontinuous Galerkin methods for high order wave equations,
  submitted to SCM
• 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