Publications 2018
1.Maximum-norms Error Estimates for High-order Finite Volume Schemes over Quadrilateral Meshes
Wenming He, Zhimin Zhang and Qingsong Zou, NUMERISCHE MATHEMATIK, 138, 2, 2018
2. A C^0 Linear Finite Element Method for Biharmonic Problems
Hailong Guo, Zhimin Zhang and Qingsong Zou, JOURNAL OF SCIENTIFIC COMPUTING, 74, 3, 2018
3. Spectral Methods for Substantial Fractional Differential Equations
Can Huang, Zhimin Zhang and Qingshuo Song, JOURNAL OF SCIENTIFIC COMPUTING, 74, 3, 2018
4. Superconvergence of Discontinuous Galerkin Method for Scalar Nonlinear Hyperbolic Equations
Waixiang Cao, Chi-wang Shu, Yang Yang and Zhimin Zhang, SIAM JOURNAL ON NUMERICAL ANALYSIS, 56, 2, 2018
5. Superconvergence Analysis of High-Order Rectangular Edge Elements for Time-Harmonic Maxwell's Equations
Ming Sun, Jichun Li, Peizhen Wang and Zhimin Zhang, JOURNAL OF SCIENTIFIC COMPUTING, 75, 1, 2018
6. Uniform l-p-bound of theallen-cahn equation and itsnumerical discretization
Yang, Jiang; Du, Qiang;Zhang, Wei, INTERNATIONALJOURNAL OFNUMERICAL ANALYSIS, 15, 1-2, 2018
7. Uniform error estimates of the conservative finite difference method for the Zakharov system in the subsonic limit regime
Yongyong Cai; Yongjun Yuan, MATHEMATICS OF COMPUTATION, 87, 311, 2018
8. A uniformly accurate (UA) multiscale time integrator pseudospectral method for the nonlinear Dirac equation in the nonrelativistic limit regime
Yongyong Cai; Yan Wang, ESAIM: MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS, 52, 2, 2018
9. Error estimates of finite difference time domain methods for the Klein-Gordon-Dirac system in the nonrelativistic limit regime
Yongyong Cai; Wenfan Yi, TIONS IN MATHEMATICAL SCIENCES, 334, 2018
10. Mathematical models and numerical methods for spinor Bose-Einstein condensates
Weizhu Bao; Yongyong Cai, COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 24, 4, 2018
11. Error estimates for a fully discretized scheme to a Cahn-Hilliard phase-field model for two-phase incompressible flows
Yongyong Cai, Jie Shen, MATHEMATICS OF COMPUTATION, 87, 2018
12. Symmetric high order Gautschi-type exponential wave integrators pseudospectral method for the nonlinear Klein-Gordon equation in the nonrelativistic limit regime
Yan Wang; Xiaofei Zhao, INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 15, 3, 2018
13. Solid-state dewetting on curved substrates
Wei Jiang; Yan Wang; David J. Srolovitz; Weizhu Bao, PHYSICAL REVIEW MATERIALS, 113401, 2018
14. Stability of the sum of two solitary waves for (gDNLS) in the energy space
Xingdong Tang and Guixiang Xu, JOURNAL OF DIFFERENTIAL EQUATIONS, 6, 264, 2018
15. Modeling Oral Multispecies Biofilm Recovery After Antibacteria Agents
Xiaobo Jing, Xiangya Huang, Markus Haapasalo, Ya Shen and Qi Wang, SCIENTIFIC REPORTS, 2018
16. he Green's function and a maximum principle for a Caputo two-point boundary value problem with a convection term
Xiangyun Meng; Martin Stynes, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 461, 1, 2018
17. Optimal error estimates of finite difference time domain methods for the Klein-Gordon-Dirac system
Wenfan Yi; Yongyong Cai, IMA JOURNAL OF NUMERICAL ANALYSIS, 2018
18. Vortex patterns and the critical rotational frequency in rotating dipolar Bose-Einstein condensates
Yongyong Cai, Yongjun Yuan, Matthias Rosenkranz, Han Pu, and Weizhu Bao, PHYSICAL REVIEW A, 023610, 2018
19. Ground states and energy asymptotics of the nonlinear Schrödinger equation with a general power nonlinearity
Xinran Ruan; Wenfan Yi, COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 24, 4, 2018
20. Efficient spectral methods for some singular eigenvalue problems
Suna Ma, Huiyuan Li and Zhimin Zhang, JOURNAL OF SCIENTIFIC COMPUTING, 77, 2018
21. An exponential time-integrator scheme for steady and unsteady inviscid flows
Shujie Li, Lishi Luo, Z.J.Wang, LiliJu, JOURNAL OF COMPUTATIONAL PHYSICS, 365, 2018
22. Error Estimates of Energy Stable Numerical Schemes for Allen–Cahn Equations with Nonlocal Constraints
Shouwen Sun, Xiaobo Jing, Qi Wang, JOURNAL OF SCIENTIFIC COMPUTING, 2018
23. Uniform Lp-bound of the Allen–Cahn equation and its numerical discretization
Qiang Du, Jiang Yang, Wei Zhang, INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 15, 1-2, 2018
24. Stabilized linear semi-implicit schemes for the nonlocal Cahn–Hilliard equation
Qiang Du, Lili Ju, Xiao Li, Zhonghua Qiao, JOURNAL OF COMPUTATIONAL PHYSICS, 363, 2018
25. A discontinuous Galerkin method for one-dimensional time-dependent nonlocal diffusion problems
Qiang Du, Lili Ju, Jianfang Lu, MATHEMATICS OF COMPUATION, 2018
26. Nonlocal Wave Propagation in Unbounded Multi-ScaleMedia
Qiang Du, Jiwei Zhang, Chunxiong Zheng, COMMUNICATIONSINCOMPUTATIONALPHYSICS, 24, 2, 2018
27. Numerical solution of a two-dimensional nonlocal wave equation on unbounded domains
Qiang Du, Houde Han, Jiwei Zhang*,, and Chunxiong Zheng, SIAM JOURNAL ON SCIENTIFIC COMPUTING, 40, 3, 2018
28. Numerical solution to a linearized time fractional KDV equation on unbounded domains
Qian Zhang, Jiwei Zhang, Shidong Jiang and Zhimin Zhang, MATHEMATICS OF COMPUTATION, 87, 310, 2018
29. Second-order Linear Schemes for Hydrodynamic Phase Field Models of Binary Viscous Fluids with Variable Densities
Gong, Yuezheng; Zhao, Jia;Yang, Xiaogang; Wang, Qi, SIAM JOURNAL ON SCIENTIFIC COMPUTING, 40, 1, 2018
30. Second Order Fully-Discrete Energy Stable Methods on Staggered Grids for Hydrodynamic Phase Field Models of Binary Viscous Fluids
Yuezheng gong, Jia Zhao, and Qi Wang, SIAM JOURNAL ON SCIENTIFIC COMPUTING, 40, 2, 2018
31. Comparison of Hydrodynamic Phase Field Models for Binary Fluid Mixtures
Xiaogang Yang, Yuezheng Gong, Jun Li, Jia Zhao, and Qi Wang, THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS, 2018
32. Asymptotically compatible schemes for stochastic homogenization
Qi Sun; Ju Ming; Qiang Du, SIAM JOURNAL ON NUMERICAL ANALYSIS, 56, 3, 2018
33. Effect of time-varying flow-shear on thenonlinear stability of the boundary ofmagnetized toroidal plasmas
Oh, Youngmin; Hwang,Hyung Ju; Leconte, Michael;Kim, Minwoo; Yun, Gunsu S.Yun, AIP ADVANCES, 8, 2, 2018
34. Convergence in positive time for a finite difference method applied to a fractional convection-diffusion equation
José Luis Gracia, Eugene O'Riordan ,Martin Stynes, COMPUT. METHODS APPL. MATH, 18, 1, 2018
35. Fractional-order derivatives defined by continuous kernels are too restrictive
Martin Stynes, APPLIED MATHEMATICS LETTERS, 85, 2018
36. Collocation methods for general Caputo two-point boundary value problems
Hui Liang, Martin Stynes, JOURNAL OF SCIENTIFIC COMPUTING, 76, 2018
37. A fitted scheme for a Caputo initial-boundary value problem
José Luis Gracia, Eugene O'Riordan , Martin Stynes, JOURNAL OF SCIENTIFIC COMPUTING, 76, 2018
38. Supercloseness of edge stabilization on Shishkin rectangular meshes for convection–diffusion problems with exponential layers
Xiaowei Liu, Martin Stynes, Jin Zhang, IMA JOURNAL OF NUMERICAL ANALYSIS, 38, 2018
39. The Numerical Computation of the TimeFractional Schrodinger Equation on anUnbounded Domain
Li, Dan; Zhang, Jiwei; Zhang,Zhimin, COMPUTATIONALMETHODS IN APPLIEDMATHEMATICS, 18, 1, 2018
40. Unconditionally Optimal Error Estimates of a Linearized Galerkin Method for Nonlinear Time Fractional Reaction-Subdiffusion Equations
Dongfang Li, Jiwei Zhang and Zhimin Zhang, JOURNAL OF SCIENTIFIC COMPUTING, 76, 2, 2018
41. Optimal Error Estimates in Numerical Solution of Time Fractional Schro04dinger Equations on Unbounded Domains
Zhizhong Sun, Jiwei Zhang, Zhimin Zhang, EAST ASIAN JOURNAL ON APPLIED MATHEMATICS, 8, 4, 2018
42. Frozen Gaussian Approximation-Based Artificial Boundary Conditions for One-Dimensional Nonlinear Schrödinger Equation in the Semiclassical Regime
Ricardo Delgadillo,Xu Yang , Jiwei Zhang, JOURNAL OF SCIENTIFIC COMPUTING, 75, 3, 2018
43. Sharp error estimate of the nonuniform L1 formula for reaction-subdiffusion equations
Honglin Liao, Dongfang Li, Jiwei Zhang, SIAM JOURNAL ON NUMERICAL ANALYSIS, 56, 2, 2018
44. An efficient second-order finite difference method for the one-dimensional Schrodinger equation with absorbing boundary conditions
Buyang Li, Jiwei Zhang, Chuxiong Zheng, SIAM JOURNAL ON NUMERICAL ANALYSIS, 56, 2, 2018
45. On the numerical solution and dynamical laws of nonlinear fractional Schrödinger/Gross-Pitaevskii equations
Xavier Antoine, Qinglin Tang, Jiwei Zhang, INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2018
46. An Efficient Spectral-Galerkin Approximation and Error Analysis for Maxwell Transmission Eigenvalue Problems in Spherical Geometries
Jing An，Zhimin Zhang, JOURNAL OF SCIENTIFIC COMPUTING, 75, 1, 2018
47. The spectral-Galerkin approximation of nonlinear eigenvalue problems
Jing An, Jie Shen, Zhimin Zhang, APPLIED NUMERICAL MATHEMATICS, 131, 2018
48. Robust Inexact Alternating Optimization for Matrix Completion with Outliers
Ji Li, Jian-Feng Cai, Hongkai Zhao, JOURNAL OF COMPUTATIONAL MATHEMATICS, 2018
49. On global convergence of gradientdescent algorithms for generalized phaseretrieval problem
Li, Ji; Zhou, Tie; Wang, Chao, JOURNAL OFCOMPUTATIONAL ANDAPPLIED MATHEMATICS, 329, 2018
50. A Petrov–Galerkin spectral method for the linearized time fractional KdV equation
Hu Chen; Tao Sun, INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 95, 6-7, 2018
51. Optimal L∞(L2) error analysis of a direct discontinuous Galerkin method for a time-fractional reaction-diffusion problem
Chaobao Huang；Martin Stynes；Na An, BIT NUMERICAL MATHEMATICS, 58, 2018
52. Uniform error bounds of a finite difference method for the Klein-Gordon-Zakharov system in the subsonic limit regime
Weizhu Bao; Chunmei Su, MATHEMATICS OF COMPUTATION, 87, 313, 2018
53. Uniform error estimates of a finite difference method for the Klein-Gordon-Schrodinger system in the nonrelativistic and massless limit regimes
Weizhu Bao; Chunmei Su, KINETIC AND RELATED MODELS, 11, 4, 2018
54. Comparison of numerical methods for the Zakharov system in the subsonic limit regime
Chunmei Su, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 330, 2018
55. A uniformly and optimally accurate method for the Zakharov system in the subsonic limit regime
Weizhu Bao; Chunmei Su, SIAM JOURNAL ON SCIENTIFIC COMPUTING, 40, 2, 2018
56. Error estimates of a finite difference method for the Klein-Gordon-Zakharov system in the subsonic limit regime
Chunmei Su; Wenfan Yi, IMA JOURNAL OF NUMERICAL ANALYSIS, 2018
57. Inverse Source Problems in Electrodynamics
Guanghui Hu, Peijun Li, Xiaodong Liu, Yue Zhao, INVERSE PROBLEMS AND IMAGING, 12, 6, 2018
58. Data-driven compressive sensing and applications in uncertainty quantification
Hong Lianga, Qi Sun,∗, Qiang Du, JOURNAL OF COMPUTATIONAL PHYSICS, 2018
59. A hybridizable discontinuous Galerkin method for elliptic interface problems in the formulation of boundary integral equations
Haixia Dong, Wenjun Ying, Jiwei Zhang, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 344, 2018
60. Acoustic scattering from corners, edges and circular cones
Joannes Elschner and Guanghi Hu, ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 228, 2, 2018
61. Inverse source problems in elastodynamics
Gang Bao, Guanghui Hu, Yavar Kian and Tao Yin, INVERSE PROBLEMS, 34, 2018
62. Inverse medium scattering from periodic structures with fixed-direction incoming waves
Peter Gibson, Guanghui Hu and Yue Zhao, INVERSE PROBLEMS, 34, 2018
63. Interface with weakly singular points always scatter
Long Li, Guanghui Hu and Jiansheng Yang, INVERSE PROBLEMS, 34, 2018
64. Determination of singular time-dependent coefficients for wave equations from full and partial data
Guanghui Hu and Yavar Kian, INVERSE PROBLEMS AND IMAGING, 12, 2018
65. Single logarithmic conditional stability in determining unknown boundaries
Johannes Elschner, Guanghui Hu and Masahiro Yamamoto, APPLICABLE ANALYSIS, 2018
Publications 2017
1. Calculating corner singularities by boundary integral equations
Hualiang Shi; Yayan Lu; Qiang Du, JOURNAL OF THE OPTICAL SOCIETY OF AMERICA, 34, 6, 2017
2. Artificial Boundary Conditions for Nonlocal Heat Equations on Unbounded Domain
Wei Zhang; Jiang Yang; Jiwei Zhang;Qiang Du, COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 21, 1, 2017
3. Mathematical and Numerical analysis of the time-dependent ginzburg-landau equations in nonconvex polygons based on hodge decomposition
Buyang Li; Zhimin Zhang, MATHEMATICS OF COMPUTATION, 86, 306, 2017
4. Efficient spectral and spectral element methods for eigenvalue problems of schrodinger equations with an inverse square potential
Huiyuan Li; Zhimin Zhang, SIAM JOURNAL OF SCIENTIFIC COMPUTING, 39, 1, 2017
5. Hessian recovery for finite element methods
Hailong Guo; Zhimin Zhang; Ren Zhao, MATHEMATICS OF COMPUTATION, 86, 306, 2017
6. Optimal Superconvergence of Energy Conserving Local Discontinuous GalerkinMethods for Wave Equations
Waixiang Cao; Dongfang Li;Zhimin Zhang, COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 21, 1, 2017
7. Superconvergence of discontinuous galerkin methods based on upwind-biased fluxes for 1d linear hyperbolic equations
Waixiang Cao; Dongfang Li; Yang Yang; Zhimin Zhang, ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS, 51, 2017
8. Spectral Galerkin methods for a weakly singular Volterra integral equation of the second kind
Can Huang; Martin Stynes, IMA JOURNAL OF NUMERICAL ANALYSIS, 37, 2017
9. Analysis and numerical solution of a Riemann-Liouville fractional derivative two-point boundary value problem
Natalia Kopteva; Martin Stynes, ADVANCES IN COMPUTATIONAL MATHEMATICS, 43, 2017
10. Error analysis of a finite difference method on graded meshes for a time-fractional diffusion equation
Martin Stynes; Eugene O’Riordan; José Luis Gracia, SIAM JOURNAL ON NUMERICAL ANALYSIS, 55,2, 2017
11. Supercloseness of continuous interior penalty method for convection–diffusion problems with characteristic layers
Jin Zhang; Martin Stynes, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 319, 2017
12. Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations:A Second-Order Scheme
Yonggui Yan;Zhizhong Sun; Jiwei Zhang, COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 22, 4, 2017
13. High Order Local Artificial Boundary Conditions for the Fractional Diffusion Equationon One-Dimensional Unbounded Domain
Wei Zhang; Can Li;Xiaonan Wu; Jiwei Zhang， JOURNAL OF MATHEMATICAL STUDY, 50, 1, 2017
14. Stability analysis for nonlinear schroordinger equations with nonlinear absorbing boundary conditions
Jiwei Zhang; Zhenli Xu; Xiaonan Wu; Desheng Wang， JOURNAL OF COMPUTATIONAL MATHEMATICS, 35, 1, 2017
15. Numerical solution to a liearized time fractional KDV equation on unbounded domains
Qian Zhang;Jiwei Zhang; Shidong Jiang; Zhimin Zhang, MATHEMATICSOFCOMPUTATION, 2017
16. A stable scheme and its convergence analysis for a 2D dynamic Q-tensor model of nematic liquid crystals
Yongyong Cai; Jie Shen; Xiang Xu, MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2017
17. Error estimates for time discretizations of Cahn-Hilliard and Allen-Cahn phase-field models for two-phase incompressible flows
Yongyong Cai; Heejun Choi; Jie Shen, NUMERISCHE MATHEMATIK, 2017
18. Numerical methods and comparison for the Dirac equation in the nonrelativistic limit regime
Weizhu Bao;Yongyong Cai; Xiaowei Jia; Qinglin Tang, JOURNAL OF SCIENTIFIC COMPUTING, 2017
19. Uniform error bounds of a finite difference method for the Klein-Gordon-Zakharov system in the subsonic limit regime
Weizhu Bao; Chunmei Su, MATHEMATICS OF COMPUTATION, 2017
20. Error estimates of a finite difference method for the Klein-Gordon-Zakharov system in the subsonic limit regime
Chunmei Su; Wenfan Yi, IMA JOURNAL OF NUMERICAL ANALYSIS, 2017
21. Global Existence and Exponential Stability for the Compressible Navier–Stokes Equations with Discontinuous Data
Huihui Kong; Hailiang Li; Chuangchuang Liang; Guojing Zhang, JOURNAL OF DIFFERENTIAL EQUATIONS, 263, 7, 2017
22. Stability of the traveling waves for the derivative Schrödinger equation in the energy space
Changxing Miao; Xingdong Tang; Guixiang Xu, CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 56, 2017
23. Symmetric High Order Gautschi-type Exponential Wave Integrators Pseudospectral Method for the Nonlinear Klein-Gordon Equation in the Nonrelativistic Limit Regime
Yan Wang; Xiaofei Zhao, INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2017
24. A NumericalAnalysis of the Weak Galerkin Method for the Helmholtz Equation with High Wave Number
Yu Du; Zhimin Zhang, COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2, 1, 2017
25. A Conservative Fourier Pseudo-Spectral Method for the Nonlinear Schrödinger Equation
Yuezheng Gong; Qi Wang; Yushun Wang; Jiaxiang Cai, JOURNAL OF COMPUTATIONAL PHYSICS, 328, 2017
26. An energy stable algorithm for a quasi-incompressible hydrodynamic phase-field model of viscous fluid mixtures with variable densities and viscosities
Yuezheng Gong; Jia Zhao; Qi Wang, COMPUTER PHYSICS COMMUNICATIONS, 219, 2017
27. Convergence of A Fast Explicit Operator Splitting Method for the Rpitaxial Growth Model with Slope Selection
Xiao Li; Zhonghua Qiao;Hui Zhang, SIAM JOURNAL ON NUMERICAL ANALYSIS , 55, 1, 2017
28. A Second-order Convex Splitting Scheme for a Cahn-Hilliard Equation with Variable Interfacial Parameters
Xiao Li; Zhonghua Qiao;Hui Zhang, JOURNAL OF COMPUTATIONAL MATHEMATICS, 35, 6, 2017
29. A discontinuous Galerkin method for stochastic Cahn–Hilliard equations
Chen Li; Ruibin Qin；Ju Ming; Zhongming Wang, COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017
30. A fully discrete direct discontinuous Galerkin method for the fractional diffusion-wave equation
Chaobao Huang; Na An; Xijun Yu, APPLICABLE ANALYSIS, 2017
31. 3-D Numerical Simulations of Biofilm Dynamics with Quorum Sensing in a Flow Cell
Jia Zhao; Qi Wang, BULLETIN OF MATHEMATICAL BIOLOGY, 79, 4, 2017
32. Preprocessing schemes for fractional-derivative problems to improve their convergence rates
Martin Stynes; José Luis Gracia, APPLIED MATHEMATICS LETTERS, 2017
33. An Efficient Spectral-Galerkin Approximation and Error Analysis for Maxwell Transmission Eigenvalue Problems in Spherical Geometries
Jing An; Zhimin Zhang, JOURNAL OF SCIENTIFIC COMPUTING, 2017
34. Blow up of Volterra Integro-Differential Equations and Applications to Semi-Linear Volterra Diffusion Equations
ZhanwenYang；TaoTang；Jiwei Zhang, Numerical NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2017
35. Superconvergence of Finite Element Approximations for the Fractional Diffusion-Wave Equation
Jincheng Ren; Xiaonan Long; Shipeng Mao; Jiwei Zhang, JOURNAL OF SCIENTIFIC COMPUTING, 2017
36. Fast Evaluation of the Caputo Fractional Derivative and its Application to Fractional Diffusion Equations
Shidong Jiang; Jiwei Zhang; Qian Zhang; Zhimin Zhang, COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2017
37. Two-Dimensional Elastic Scattering Coefficients and Enhancement of Nearly Elastic Cloaking
Tasawar Abbas; Habib Ammari; Guanghui Hu; Abdul Wahab; Jong Chul Ye, JOURNAL OF ELASTICITY, 2017
38. Superconvergence of Immersed Finite Volume Methods for One-Dimensional Interface Problems
Cao, Waixiang; Zhang, Xu; Zhang, Zhimin; Zou, Qingsong, JOURNAL OF SCIENTIFIC COMPUTING, 2017
39. A C-0 linear finite element method for two fourth-order eigenvalue problems
Chen, Hongtao; Guo, Hailong; Zhang, Zhimin; Zou, Qingsong, IMA JOURNAL OF NUMERICAL ANALYSIS, 2017
40. Superconvergence of immersed finite element methods for interface problems
Cao, Waixiang; Zhang, Xu; Zhang, Zhimin, ADVANCES IN COMPUTATIONAL MATHEMATICS, 2017
41. A Numerical Analysis of the Weak Galerkin Method for the Helmholtz Equation with High Wave Number
Yu Du, Zhimin Zhang, COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2017
42. A Hybridzable Weak Galerkin Method for the Helmholtz Equation with Large Wave Number:hp analysis
Jiangxing Wang, Zhimin Zhang, INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2017
43. A C0 Linear Finite Element Method for Biharmonic Problems
Hailong Guo, Zhimin Zhang, Qingsong Zou, JOURNAL OF SCIENTIFIC COMPUTING, 2017
44. Numerical Solution of the Time-Fractional Sub-Diffusion Equation on an Unbounded Domain in Two-Dimensional Space
Li, Hongwei; Wu, Xiaonan; Zhang, Jiwei, EAST ASIAN JOURNAL ON APPLIED MATHEMATICS, 2017
45. On global convergence of gradient descent algorithms for generalized phase retrieval problem
Ji Li;Zhou Tie; Chao Wang, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2017
Publications 2016
1 The velocity tracking problem for Wick-stochastic Navier-Stokes flows using Weiner chaos expansion
Hong Liang, Lisheng Hou, Ju Ming; Journal of Computational and Applied Mathematics; 307, 25-36 (2016)
2 A recovery based linear finite element method for 1D Bi-Harmonic problems
Hongtao Chen, Zhimin Zhang, Qingsong Zou; Journal of Scientific Computing; 68, 1, 375-394 (2016)
3 Efficient implementation to numerically solve the nonlinear time fractional parabolic problems on unbounded spatial domain
Dongfang Lia, Jiwei Zhang; Journal of Computational Physics; 322, 415-428 (2016)
4 Mean-field regime and Thomas-Fermi approximations of trapped Bose-Einstein condensates with higher-order interactions in one and two dimensions
Xinran Ruan, Yongyong Cai, Weizhu Bao; Journal of Physics B-Atomic Molecular and Optical Physics; 49, 12 (2016)
5 Superconvergence of local discontinuous galerkin methods for one-dimensional linear parabolic equations
Waixiang Cao, Zhimin Zhang; Mathematics of Computation; 85, 63-84 (2016)
6 Hydrodynamic theories for flows of active liquid crystals and the generalized onsager principle
Xiaogang Yang, Jun Li, M. Gregory Forest, Qi Wang; Entropy; 18, 6 (2016)
7 A 3D multi-phase hydrodynamic model for cytokinesis of eukaryotic cells
Jia Zhao, Qi Wang; Communications in Computational Physics; 19, 3, 663-681 (2016)
8 Numerical blow-up of nonlinear parabolic integro-differential equations on unbounded domain
Hermann Brunner, Tao Tang, Jiwei Zhang; Journal of Scientific Computing; 68, 1281-1298 (2016)
9 Stochastic Steady-State Navier-Stokes Equations with Additive Random Noise
Max D.Gunzburger, Lisheng Hou, Ju Ming; Journal of Scientific Computing; 66, 2, 672-691 (2016)
10 A decoupled energy stable scheme for a hydrodynamic phase-field model of mixtures of nematic liquid crystals and viscous fluids
Jia Zhao, Xiaofeng Yang, Jie Shen, Qi Wang; Journal of Computational Physics; 305, 539-556 (2016)
11 Error estimates in the energy space for a Gautschi-type integrator spectral discretization for the coupled nonlinear Klein-Gordon equations
Zhiguo Xu, Xuanchun Dong, Yongjun Yuan; Journal of Computational and Applied Mathematics; 292, 402-416 (2016)
12 Numerical shooting methods for optical boundary control and exact boundary control of 1-D wave equations
L.Steven Hou, Ju Ming, Sung-Dae Yang; International Journal of Numerical Analysis and Modeling; 13, 1, 122-144 (2016)
13 Superconvergence points of fractional spectral interpolation
Xuan Zhao, Zhimin Zhang; SIAM Journal on Scientific Computing; 38, 1, A598-A613 (2016)
14 Role of the active viscosity and self-propelling speed in channel flows of active polar liquid crystals
Xiaogang Yang, Qi Wang; Soft Matter; 12, 4, 1262-1278 (2016)
15 Optimization-based shrinking dimer method for finding transition states
Lei Zhang, Qiang Du, Zhenzhen Zheng; SIAM Journal on Scientific Computing; 38, 1, A528- A544 (2016）
16 Superconvergence of the Direct Discontinuous Galerkin Method for Convection-Diffusion Equations
Waixiang Cao; Hailiang Liu;Zhimin Zhang, NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2016
17 Boundary layers in a Riemann-Liouville fractional derivative two-point boundary value problem
J.L.Gracia, M. Stynes; Lecture Notes in Computational Science and Engineering; 108, 87-98 (2016)
18 Blow-up of solutions and interior layers in a Caputo two-point boundary value problem
M. Stynes, J.L.Gracia; Lecture Notes in Computational Science and Engineering; 108, 293-302 (2016)
19 A uniformly accurate multiscale time integrator pseudospectral method for the Dirac equation in the nonrelativistic limit regime
Weizhu Bao,Yongyong Cai, Xiaowei Jia, Qinglin Tang; SIAM J. Numer. Anal.; 54, 3, 1785-1812 (2016)
20 Efficient implementation to numerically solve the nonlinear time fractional parabolic problems on unbounded domain
Jiwei Zhang, Dan Li; Journal of Computational Physics; 322, 415-428 (2016)
21 A domain decomposition method for the steady-state Navier-Stokes Darcy model with Beavers-Joseph interface condition
Ju Ming; SIAM Journal on Scientific Computing; 37, 5, 264-290 (2016)
22 The multi-level Monte Carlo method for simulations of turbulent flows
Ju Ming; Monthly Weather Review (2016)
23 Multi-Level Monte Carlo Method for A Stochastic Optimal Control Problem
Ju Ming; SIAM Journal on UQ (2016)
24 Necessary Conditions for Convergence of Difference Schemes for Fractional-Serivative Two-Point Boundary Value Problems
Martin Stynes, E.O'Riordan & J.L.Gracia；Bit Numerical Mathematics; 56, 4, 1455-1477 (2016)
25 A Caputo Two-Point Boundary Value Problem: Existence, Uniqueness and Regularity of A Solution
Martin Stynes; Modelling and Analysis Information System; 23, 3, 370-376 (2016)
26 A Spectral Collocation Method for A Weakly Singular Volterra Integral Equation of the Second Kind
Huang, Can & Martin Stynes; Advanced Computational Mathematics; 42, 5, 1015-1030 (2016)
27 Superconvergent Two-Grid Methods for Elliptic Eigenvalue Problems
Hailong Guo; Zhimin Zhang; Ren Zhao, SIAM JOURNAL ON SCIENTIFIC COMPUTING, 70, 2016
28 Mathematical and Numerical Analysis of Time-Dependent Ginzburg--Landau Equations in Nonconvex Polygons
Li, Buyang, Zhang, Zhimin；Mathematics of Computation; (2016)
29 Numeircal Solution to A Linearized Time Fractional KDV Equation on Unbounded Domains
Zhang, Qian, Zhang, Jiwei, Jiang, Shidong, Zhang, Zhimin; Mathematics of Computation; (2016)
30 Optimal Superconvergence of Energy Conserving Local Discontinuous Galerkin Methods for Wave Equations
Cao, Waixiang, Li, Dongfang, Zhang, Zhimin; Communication in Computational Physics; (2016)
31 Ultraconvergence of Finite Element Method by Richardson Extrapolation for Elliptic Problems with Constant Coefficients
He, Wenming, Lin, Runchang, Zhang, Zhimin; Numerical Analysis; 54, 4, 2302-2322 (2016)
32 Fully Discretized Energy Stable Schemes for Hydrodynamic Equations Governing Two-Phase Viscous Fluid Flows
Gong, Yuezheng, Liu, Xinfeng, Wang, Qi; Journal of Scientific Computing; 69, 921-945 (2016)
33 Convergence outside the initial layer for a numerical method for the time-fractional heat equation
Jose Luis Gracia; Eugene O'Riordan;Martin Stynes, INTERNATIONAL CONFERENCE ON NUMERICAL ANAYSIS & ITS APPLICATIONS, 2016
34 Structure-Preserving Galerkin POD Reduced-Order Modeling of Hamiltonian Systems
Gong, Yuezheng, Wang, Qi, Wang, Zhu; Computational Methods in Applied Mechanics and Engineering; (2016)
35 Modeling Antimicrobial Tolerance and Treatment of Heterogeneous Biofilms
Zhao, Jia, P Seeluangsawat, Wang, Qi; Mathematical Biosciences; 282, 1-15 (2016)
36 Energy Stable Numerical Schemes for A Hydrodynamic Model of Nematic Liquid Crystals
Zhao, Jia, Yang, Xiaogang, Li, Jun, Wang, Qi；SIAM Journal on Scientific Computing; 38, 5, A3264-A3290 (2016)
39 Numerical Approximations to A New Phase Field Model for Two Phase Flows of Complex Fluids
Zhao, Jia, Wang, Qi, Yang, Xiaogang；Computational Methods in Applied Mechanics and Engineering; 310, 77-97 (2016)
40 A Numerical Study of Complex Reconstruction in Inverse Elastic Scattering
Guanghui Hu; Jingzhi Li;, Hongyu Liu; Qi Wang, COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 19, 5, 2016
41 Too much regularity may force too much uniqueness
Martin Stynes, FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 19, 6, 2016
42 Symmetric High Order Gautschi-type Exponential Wave Integrators Pseudospectral Method for the Nonlinear Klein-Gordon Equation in the Nonrelativistic Limit Regime
Wang, Yan, Zhao Xiaofei; International Journal of Numerical Analysis and modeling; (2016)
43 Artificial Boundary Conditions for Nonlocal Heat Equations on Unbounded Domain
Zhang, Wei, Zhang, Jiwei, Du, Qiang; Communications in Computational Physics; 21, 1, 16, 39 (2016)
44 A Numerical Analysis of the Weak Galerkin Method for the Helmholtz Equation with High Wave Number
Du, Yu, Wu, Haijun, Zhang, Zhimin; Communications in Computational Physics; (2016)
45. Structure-Preserving Galerkin POD Reduced-Order Modeling of Hamiltonian Systems
Yuezheng Gong; Qi Wang; Zhu Wang, COMPUTATIONAL METHODS IN APPLIED MECHANICS AND ENGINEERING, 315, 2016
Publications 2015
1 解一维双曲守恒律方程和抛物方程的间断有限元法的逐点和区间平均值误差估计
Waixiang Cao and Zhimin Zhang; Scientia Sinica Mathematica; 45, 8, 1115-1132 (2015)
2 Gradient recovery for the grouzeix–raviart element
Hailong Guo and Zhimin Zhang; Journal of Scientific Computing; 64, 2, 456-476 (2015)
3 Superconvergence of discontinuous galerkin method for two-dimensional hyperbllic equations
Waixiang Cao, Chi-Wang Shu, Yang Yang and Zhimin Zhang; SIAM Journal on Numerical Analysis; 53, 4, 1651–1671 (2015)
4 Structure Formation in Sheared Polymer-Rod Nanocomposites
Guanghua Ji, M. G. Forest, and Qi Wang; Discrete and Continuous Dynamical Syestems Series-S; 8, 2 (2015)
5 Analytic Oncology
Hua Jiang, Hao Yang, Jun Zeng, Zhiyuan Zhou, Jin Peng and Qi Wang; Electron J Metab Nutr Cancer; 2, 2 (2015)
6 Is 2k-conjecture valid for finite volume methods?
Waixiang Cao, Zhimin Zhang and Qingsong Zou; SIAM Journal on Numerical Analysis; 53, 2, 942-962 (2015)
7 Nonlocal convection-diffusion problems and finite element approximations
Hao Tian, Lili Ju and Qiang Du; Computer Methods in Applied Mechanics and Engineering; 289, 60-78 (2015)
8 Boundary layers in a two-point boundary value problem with a Caputo fractional derivative
M.Stynes & J.L.Gracia; Comput.Methods Appl. Math. ; 15, 1, 79-95 (2015)
9 Superconvergence of discontinuous Galerkin methods for linear hyperbolic equations
Waixiang Cao, Zhimin Zhang, Qingsong Zou; Siam Journal on Numerical Analysis; 53, 5 (2015)
10 Analysis of a p-version finite volume method for 1-D elliptic problems
Waixiang Cao, Zhimin Zhang, Qingsong Zou; Journal of Computational and Applied Mathematics; 265 (2015)
11 A robust residual-type a posteriori error estimator for convection-diffusion equations
Shaohong Du, Zhimin Zhang; Journal of Scientific Computing; 65, 1, 138-170 (2015)
12 How many numerical eigenvalues can we trust?
Zhimin Zhang; Journal of Scientific Computing; 65, 2, 455-466 (2015)
13 Some recent advances on vertex centered finite volume element methods for elliptic equations
Zhimin Zhang, Qingsong Zou; Science China Mathematics; 56, 12 (2015)
14 A family of finite volume schemes of arbitrary order on rectangular meshes
Zhimin Zhang, Qingsong Zou; Journal of Scientific Computing; 58, 2 (2015)
15 Vertex-centered finite volume schemes of any order over quadrilateral meshes for elliptic boundary value problems
Zhimin Zhang, Qingsong Zou; Numerische Mathematik; 130, 1, 363-393 (2015)
16 Superconvergence of lacal discontinuous galerkin methods for one-dimensional linear parabolic equations
Waixiang Cao, Zhimin Zhang; Mathematics of Computation; 85, 297, 63-84 (2015)
17 Superconvergence points of polynomial spectral interpolation
Zhimin Zhang; SIAM Journal on Numerical Analysis; 50, 6 (2015)
18 A spectral collocation method for eigenvalue problems of compact integral operators
Can Huang, Hailong Guo, Zhimin Zhang; Journal of Integral Equattions and Applications; 25, 1 (2015)
19 Finite volume superconvergence approximation for one-dimesional singularly perturbed problems
Waixiang Cao, Zhimin Zhang, Qingsong Zou; Journal of Computational Mathematics; 31, 5 (2015)
20 Superconvergence of jacobi-gauss-type spectral interpolation
Lilian Wang, Xiaodan Zhao, Zhimin Zhang; Journal of Scientific Computing; 59, 3 (2015)
21 Space-time discontinuous Galerkin method for Maxwell equations in dispersive media
Bo Wang, Ziqing Xie, Zhimn Zhang; Acta Mathematica Scientia; 34(B), 5 (2015)
22 Polynomial preserving recovery of an over-penalized symmetric interior penalty Galerkin method for elliptic problems
Lunji Song, Zhimin Zhang; Discrete and Continuous Dynamical Systems Series B; 20, 5, 1405-1426 (2015)
23 Superconvergence property of an over-penalized discontinuous Galerkin finite element gradient recovery method
Lunji Song, ZhiminZhang; Journal of Computational Physics; 299, C, 1004-1020 (2015)
24 Local error estimates of the LDG method for 1-D singulary perturbed problems
Huiqing Zhu, Zhimin Zhang; International Journal of Numerical Anaysis and Modeling; 10, 2 (2015)
25 Pointwise error estimates for the LDG method applied to 1-D singularly perturbed reaction-diffusion problems
Huiqing Zhu, Zhimin Zhang; Computational Methods in Applied Mathematics; 13, 1 (2015)
26 The spectral collocation method for stochastic differential equations
Can Huang, Zhimin Zhang; Discrete and Continuous Dynamical Systems Series B; 18, 3 (2015)
27 Spectral collocation method for differential-algebraic equations with arbitrary index
Can Huang, Zhimin Zhang; Journal of Scientific Computing; 58, 3 (2015)
28 Superconvergence of conforming finite element method for fourth-order singularly perturbed problems of reaction-diffusion type in 1-D
Hailong Guo, Can Huang, Zhimin Zhang; Numerical Methods for Partial Differential Equations; 30, 2 (2015)
29 Uniform convergence of the LDG method for a singularly perturbed problem with the exponential boundary layer
Huiqing Zhu, Zhimin Zhang; Mathematics of Computation; 83, 286 (2015)
30 The long time behavior of a spectral collocation method for delay differential equations of pantogrph type
Jie Tang, Ziqing Xie, Zhimin Zhang; Discrete and Continuous Dynamical Systems Series B; 18, 3 (2015)
31 A new approach for numerical simulation of the time-dependent Ginzburg–Landau equations
Buyang Li, Zhimin Zhang; Journal of Computational Physics; 303, 250-283 (2015)
32 Covergence of a p-version / hp-version method for fractional differential equations
Can Huang and Zhimin Zhang; Journal of Computational Physics; 286, 118-127 (2015)
33 On the spectrum computation of non-oscillatory and highly oscillatory kernel with weak singularity
Can Huang, Zhimin Zhang; Journal of Scientific Computing; 63, 1, 1-22 (2015)
34 Special section on differential equations: Theory, application, and numerical approximation
Yanzhao Cao, Anping liu, Zhimin Zhang; Discrete and Continuous Dynamical Systems Series B; 20, 5, I-II (2015)
35 A New Adaptive Mixed Finite Element Method Based on Residual Type A Posterior Error Estimates for the Stokes Eigenvalue Problem
Jiayu Han, Zhimin Zhang, Yidu Yang; Numerical Methods for Partial Differential Equations; 31, 1, 31-53 (2015)
36 3-D Spatial-Temporal Structures of Biofilms in A Water Channel
Chen Chen, Dacheng Ren, Mingming Ren, Qi Wang; Mathematical Methods in Applied Sciences; 38, 18, 4461-4478 (2015)
37 An efficient collocation method for a Caputo two-point boundary value problem
N.Kopteva, M. Stynes; BIT Numer. Math; 55, 1105-1123 (2015)
38 A balanced finite element method for a system of singularly perturbed reaction-diffusion two-point boundary value problems
R.Lin, M. Stynes; Numer. Algorithms; 70, 4, 691-707 (2015)
39 Some open questions in the numerical analysis of singularly perturbed differential equations
H.-G.Roos, M. Stynes; Comput. Methods Appl. Math; 15, 4, 531-550 (2015)
Publications 2014
1 Superconvergence of discontinuous Galerkin methods for linear hyperbolic equations
Waixiang Cao, Zhimin Zhang and Qingsong Zou; SIAM Journal on Numerical Analysis; 52, 5, 2555-2573 (2014)
2 Analysis of a p-version finite volume method for 1-D elliptic problems
Waixiang Cao, Zhimin Zhang and Qingsong Zou; Journal of Computational and Applied Mathematics ; 265, 17-32 (2014)
3 Near equilibrium dynamics and 1-D spatial-temporal structures of polar active liquid crystals
Xiaogang Yang, M. G. Forest, and Qi Wang; Chinese Phys. B; 23, 11, 118701 (2014)
4 Efficient Implementation of a Spectral-Tau Method
Fei Liu; Journal of Mathematical Study; (2014)
5 A robust residual-type a posteriori error estimator for convection-diffusion equations
Shaohong Du and Zhimin Zhang; Journal of Scientific Computing; 61, 3, 138-170 (2014)
6 Stability and convergence of trigonometric integrator pseudospectral discretization for N-coupled nonlinear Klein-Gordon equations
Xuanchun Dong; Applied Mathematics and Computation; 232, 752-765 (2014)
7 How many numerical eigenvalues can we trust?
Zhimin Zhang; Journal of Scientific Computing ; 65, 2, 455-466 (2014)
8 Stochastic steady-state navier–stokes equations with additive random noise
Lisheng Hou, Max Gunzburger and Ju Ming; Journal of Scientific Computing, DOI; 258, 538-554 (2014)
9 Numerical solution of the nonlinear Schr¨odinger equation with wave operator on unbounded domains
Hongwei Li, Xiaonan Wu, and Jiwei Zhang; Physical Review E; 90, 3 (2014)
10 A family of finite volume schemes of arbitrary order on rectangular meshes
Zhimin Zhang and Qingsong Zou; Journal of Scientific Computing ; 58, 2, 308-330 (2014)
11 An efficient spectral method for computing dynamics of rotating two-component Bose-Einstein condensates via coordinate transformation
Ju Ming; Qinglin Tang; Yanzhi Zhang; Journal of Computational Physics; 258, 538-554 (2014)
12 A fast and faithful collocation method with efficient matrix assemebly by a two-dimensional nonlocal diffusion model
Hong Wang and Hao Tian; Computer Methods in Applied Mechanics and Engineering; 273, 19-36 (2014)
13 On time-splitting pseudospectral discretization for nonlinear Klein-Gordon equation in nonrelativistic limit regime
Xuanchun Dong, Zhiguo Xu and Xiaofei Zhao; Communications in Computational Physics; 16, 2, 440-446 (2014)
14 Sharp anisotropic interpolation error estimates for rectangular Raviart-Thomas elements
Martin Stynes; Mathematics of Computation ; 83, 290, 2675-2689 (2014)
15 Numerical solution of the nonlinear Schrodinger equation with wave operator on unbounded domains
J. Zhang, H. Li, X. Wu; Phys. Rev. E; 90, 3 (2014)
Publications 2013-2012
1 Error reduction of the adaptive conforming and nonconforming finite element methods with red-green refinement
Zhongci Shi and Xuying Zhao; Numerische Mathematik; 123, 3 (2013)
2 Numerical methods and comparison for computing dark and bright solitons in the nonlinear Schrodinger equation
Weizhu Bao, Qinglin Tang, Zhiguo Xu; Journal of Computational Physics; 235 (2013)
3 Analysis and computation for ground state solutions of bose-fermi mixtures at zero temperature
Yongyong Cai and Hanquan Wang; SIAM Journal on Applied Mathematics; 73, 2 (2013)
4 Some recent advances on vertex centered finite volume element methods for elliptic equations
Zhimin Zhang and Qingsong Zou; Science China Mathematics; 56, 12, 2507–2522 (2013)
5 A numerical study of the ground state and dynamics of atomic-molecular bose-einstein condensates
Wei Jiang, Hanquan Wang and Xianggui Li; Computer Physics Communications; 184, 11 (2013)
