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:
Mahematics 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. Mathematics, University of Science and Technology of China, 1982
- M.S. Computational Mathematics, University of Science and Technology of China, 1985
- Ph.D., 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.
Citation index
https://scholar.google.com/citations?user=kwy7ROYAAAAJ&hl=en