Zhimin Zhang
- Professor, since 2002, Wayne State University (WSU)
- Associate professor, 1999-2002, WSU
- Associate professor, 1997-2000, Texas Tech University (TTU)
- Assistant professor (tenure track), 1993-1997, TTU
- Visiting assistant professor, 1991-1993, TTU
Research interest(s)/area of expertise
- Numerical analysis, computational mathematics, scientific computing
- Numerical methods for partial differential equations including finite element methods, finite volume methods, spectral methods
Research
Associate editor or editorial board member:
- Mathematics of Computation, 2009-2017
- Journal of Scientific Computing, 2011-2017
- Journal of Computational Mathematics, 2007-2023
- Discrete and Continuous Dynamical Systems – Series B, since 2003
- International Journal of Numerical Analysis & Modeling, since 2004
- Mathematical Culture, since 2008
- Journal of Mathematical Study, since 2013
- Numerical Methods for Partial Differential Equations, since 2013
- Communications on Applied Mathematics and Computation, since 2018
- CSIAM Transaction on Applied Mathematics, since 2019
Education
- B.S. in Mathematics, University of Science and Technology of China, 1982
- M.S. in Computational Mathematics, University of Science and Technology of China, 1985
- Ph.D. in Applied Mathematics, University of Maryland at College Park, 1991
Awards and grants
- 2011 Outstanding Graduate Mentor Award, Wayne State University
- 2014 Charles H. Gershenson Distinguished Faculty Fellows Award, Wayne State University
- PI for National Scince Fundaton grants since 2003
- DMS-0311807, "Recovery Type A Posteriori Error Estimates"
- DMS-0612908, "Superconvergence of p-Version / Spectral Collocation, Discontinuous Galerkin Methods and Eigenvalue Approximation"
- DMS-1115530, "Spectral and Spectral Collocation Methods for Hamiltonian Systems"
- DMS-1419040, "Superconvergent Post-processing of Some Newly Developed Numerical Methods with Weak Derivatives"
Selected publications
- Lixiu Wang, Qian Zhang, and Zhimin Zhang, Superconvergence analysis of curlcurl-conforming elements on rectangular meshes, Journal of Scientific Computing, 95-2 (2023), 23
- Dongfang Li, Xiaoxi Li, and Zhimin Zhang, Implicit-explicit relaxation Runge-Kutta methods: construction, analysis and applications to pdes, Mathematics of Computation, 92-339 (2023), 117-146
- Wei Wang and Zhimin Zhang, Spectral element methods for eigenvalue problems based on domain decomposition, SIAM Journal on Scientific Computing, 44-2 (2022), A689-A719
- Kaibo Hu, Qian Zhang, and Zhimin Zhang, A family of finite element Stokes complexes in three dimensions, SIAM Journal on Numerical Analysis, 60-1 (2022), 222-243. (SIAM high impact paper)
- Baoli Yin, Yang Liu, Hong Li, and Zhimin Zhang, Efficient shifted fractional trapezoidal rule for subdiffusion problems with nonsmooth solutions on uniform meshes, BIT Numerical Mathematics, 62-2 (2022), 631-666
- Waixiang Cao, Lueling Jia, and Zhimin Zhang, A $C^1$ conforming Petrov-Galerkin method for convection-diffusion equations and superconvergence analysis over rectangular meshes, SIAM Journal on Numerical Analysis, 60-1 (2022), 274-311
- Yang Liu, Baoli Yin, Hong Li, and Zhimin Zhang, The unified theory of shifted convolution quadrature for fractional calculus, Journal of Scientific Computing, 89 (2021), 18
- Zhaopeng Hao, Huiyuan Li, Zhimin Zhang, and Zhongqiang Zhang, Sharp error estimates of a spectral Galerkin method for a diffusion-reaction equation with integral fractional Laplacian on a disk, Mathematics of Computation, 90 (2021), 2107-2135
- Beiping Duan and Zhimin Zhang, A rational approximation scheme for computing Mittag-Leffler function with discrete elliptic operator as input, Journal of Scientific Computing, 87 (2021), 75
- Hong-lin Liao and Zhimin Zhang, Analysis of adaptive BDF2 scheme for diffusion equations, Mathematics of Computation, 90-329 (2021), 1207-1226
- Qian Zhang and Zhimin Zhang, A family of curl-curl conforming finite elements on tetrahedral meshes, CSIAM Transactions on Applied Mathematics,1-4 (2020), 639-663
- Kaibo Hu, Qian Zhang, and Zhimin Zhang, Simple curl-curl-conforming finite elements in two dimensions, SIAM Journal on Scientific Computing, 42-6 (2020), A3859-A3877
- Jing An, Waixiang Cao, and Zhimin Zhang, A class of efficient spectral methods and error analysis for nonlinear Hamiltonian systems, Communications in Mathematical Sciences, 18-2 (2020), 395-428
- Jing An, Waixiang Cao, and Zhimin Zhang, An efficient spectral Petrov-Galerkin method for nonlinear Hamiltonian systems, Communications in Computational Physics, 26-5(2019), 1249-1273
- Jiguang Sun, Qian Zhang, and Zhimin Zhang, A curl-conforming weak Galerkin method for the quad-curl problem, BIT Numerical Mathematics 59(2019), 1093-1114
- Jun Hu, Shangyou Zhang, and Zhimin Zhang, On the $2p$th-order of convergence of the Galerkin difference method, SIAM Journal on Numerical Analysis 57-5(2019), 2189-2199
- Qian Zhang, Lixiu Wang, and Zhimin Zhang, $H(curl^2)$-conforming finite elements in 2D and applications to the quad-curl problem, SIAM Journal on Scientific Computing 41-3 (2019), A1527-A1547
- Yu Du, Lu Zhang, and Zhimin Zhang, Convergence analysis of a discontinuous Galerkin method for wave equations in second-order form, SIAM Journal on Numerical Analysis 57-1 (2019), 238-265
- Waixiang Cao and Zhimin Zhang, Some recent developments in superconvergence of discontinuous Galerkin methods for time-dependent partial differential equations, Journal of Scientific Computing 77 (2018), 1402-1423
- Hailong Guo, Xu Yang, and Zhimin Zhang, Superconvergence analysis of partially penalized immersed finite element methods, IMA Journal of Numerical Analysis 38-4 (2018), 2123-2144
- Waixiang Cao, Chi-Wang Shu, Yang Yang, and Zhimin Zhang, Superconvergence of discontinuous Galerkin method for scalar nonlinear hyperbolic equations, SIAM Journal on Numerical Analysis 56-2 (2018) 732-765
- Hailong Guo, Zhimin Zhang, and Qingsong Zou, A $C^0$ linear finite element method for biharmonic problems, Journal of Scientific Computing 74 (2018), 1397-1422
- Wenming He, Zhimin Zhang, and Qingsong Zou, Maximum-norms error estimates for high-order finite volume schemes over quadrilateral meshes, Numerische Mathematik 138 (2018), 473-500
- Qian Zhang, Jiwei Zhang, Shidong Jiang, and Zhimin Zhang, Numerical solution to a linearized time fractional KDV equation on unbounded domains, Mathematics of Computation 87-310 (2018), 693-719
- Shidong Jiang, Jiwei Zhang, Qian Zhang, and Zhimin Zhang, Fast evaluation of the Caputo fractional derivative and its applications to fractional diffusion equations, Communication in Computational Physics 21-3 (2017), 650-678
- Wenming He and Zhimin Zhang, $2k$ superconvergence of $Q_k$ finite elements by anisotropic mesh approximation in weighted Sobolev spaces, Mathematics of Computation 86 (2017), 1693-1718
- Hongtao Chen, Hailong Guo, Zhimin Zhang, and Qingsong Zou, A $C^0$ linear finite element method for two forth-order eigenvalue problems, IMA Journal of Numerical Analysis 37-4 (2017), 2120-2138
- Wenming He, Zhimin Zhang, and Qingsong Zou, Ultraconvergence of high order FEMs for elliptic problems with variable coefficients, Numerische Mathematik 136-1 (2017), 215-248
- Hailong Guo, Zhimin Zhang, and Ren Zhao, Hessian recovery for finite element methods, Mathematics of Computation 86 (2017), No.306, 1671-1692
- Buyang Li and Zhimin Zhang, Mathematical and numerical analysis of the time-dependent Ginzburg-Landau equations in nonconvex polygons based on Hodge decomposition, Mathematics of Computation 86 (2017), No.306, 1579-1608
- Huiyuan Li and Zhimin Zhang, Efficient spectral and spectral element methods for eigenvalue problems of Schrodinger equations with an inverse square potential, SIAM Journal on Scientific Computing 39-1 (2017), A114-A140
- Wenming He, Runchang Lin, and Zhimin Zhang, Ultraconvergence of finite element method by Richardson extrapolation for elliptic problems with constant coefficients, SIAM Journal on Numerical Analysis 54-4 (2016), 2302-2322
- Waixiang Cao and Zhimin Zhang, Superconvergence of local discontinuous Galerkin method for one-dimensional linear parabolic equations, Mathematics of Computation 85 (2016), 63-84
- Xuan Zhao and Zhimin Zhang, Superconvergence points of fractional spectral interpolation, SIAM Journal on Scientific Computing 38-1 (2016), A598-A613
- Qingsong Zou and Zhimin Zhang, Vertex-centered finite volume schemes of any order over quadrilateral meshes for elliptic boundary value problems. Numerische Mathematik 130 (2015), 363-393
- Buyang Li and Zhimin Zhang, A new approach for numerical simulation of the time-dependent Ginzburg-Landau equations, Journal of Computational Physics 303 (2015), 238-250
- Zhimin Zhang, How many numerical eigenvalues can we trust? Journal of Scientific Computing 65-2 (2015), 455-466
- Waixiang Cao, Zhimin Zhang, and Qingsong Zou. Superconvergence of Discontinuous Galerkin method for linear hyperbolic equations, SIAM Journal on Numerical Analysis 52-5 (2014), 2555-2573
- Zhimin Zhang, Superconvergence points of polynomial spectral interpolation. ,SIAM Journal on Numerical Analysis 50-6 (2012), 2966-2985
- Runchang Lin and Zhimin Zhang, Natural superconvergent points in 3Dfinite elements, SIAM Journal on Numerical Analysis 46-3 (2008), 1281-1297
- Zhimin Zhang and Ahmed A. Naga, A new finite element gradient recovery method: Superconvergence property, SIAM Journal on Scientific Computing 26-4 (2005), 1192-1213
- Zhimin Zhang, Finite element superconvergence on Shishkin mesh for 2-D convection-diffusion problems, Mathematics of Computation 72 (2003), 1147-1177