姓名：李猛
研究领域：有限元方法、虚拟元方法、谱方法以及配置方法，目前主要研究曲率流模型、量子力学模型的保结构算法，以及机器学习等。
邮箱：limeng@zzu.edu.cn
简要经历
2022.08-2023.08访问新加坡国立大学，访问学者，导师：包维柱院士
2017年7月至今，郑州大学数学与统计学院，副教授
2017年6月博士毕业于华中科技大学数学与统计学院，导师：黄乘明教授
主要项目
1. 中国博士后科学基金第16批特别资助（站中），2023/01-2023/12
2. 国家自然科学基金青年项目，几类分数阶偏微分方程的虚拟有限元方法，2019/01-2021/12
3. 第63批中国博士后科学基金面上项目，几类非线性时间分数阶模型的高精度无网格比有限元方法，2019/01-2020/12
4. 省科技厅项目，分数阶 Ginzburg-Landau 方程的快速有限元方法研究，2019/01-2020/12
5. 国家自然科学基金委员会，中俄合作交流项目，分数阶偏微分方程的高阶数值方法，2020/01-2021/12
奖励
1. 入选美国斯坦福大学发布的2024全球前2%科学家
2. 河南省自然科学奖二等奖，河南省人民政府
3. 河南省教育厅科技成果奖优秀科技论文奖，省部一等奖（2021，2023，2024）
4. 河南省优秀学位论文指导教师（硕士、学士）
5. 博士研究生国家奖学金
6. 华中科技大学优秀毕业研究生
7. 郑州大学优秀党员
8. 2023河南省突出贡献奖，河南省人力资源和社会保障厅
其他
目前担任中国计算物理学会理事,中国仿真算法专业委员会委员
论著
《数值分析》，国家开放大学出版社，2021.（河南省“十四五”普通高等教育规划教材）
论文
2025
[1] Meng Li, Chunjie Zhou. Structure-preserving parametric finite element methods for simulating axisymmetric solid-state dewetting problems with anisotropic surface energies. Journal of Computational Physics, 2025, 531: 113944.
[2] Meng Li, Junjun Wang, Zhen Guan, Zhijie Du, Structure-preserving finite element methods for computing dynamics of rotating Bose-Einstein condensate. ESAIM Mathematical Modelling and Numerical Analysis, 2025, 59: 519-552.
[3] Meng Li, Chunjie Zhou, Energy-stable parametric finite element approximations for regularized solid-state dewetting in strongly anisotropic materials. Journal of Nonlinear Science, 2025, 35: 52.
[4] Zhenghua Duan, Meng Li*, Chunjie Zhou, Solid-state dewetting of axisymmetric thin film on axisymmetric curved-surface substrates: Modeling and simulation. Physica D, 2025, 481: 134871.
[5] Meng Li, You Yang, A structure-preserving PINN with embedded periodic boundary layer and adaptively enforced initial conditions for geometric flows. Computer Physics Communications, 2025, 316: 109762.
[6] Yihang Guo, Meng Li*, Structure-preserving parametric finite element methods for anisotropic surface diffusion flow with minimal deformation formulation. Computer Physics Communications, 2025, 313: 109620.
[7] Meng Li, Yifei Li, Energy-stable parametric finite element methods for the generalized Willmore flow with axisymmetric geometry: closed surfaces. Communications in Computational Physics, 2025, DOI: 10.4208/cicp.OA-2024-0268.
[8] Meng Li, Error analysis of finite element approximation for mean curvature flows in axisymmetric geometry. Journal of Scientific Computing, 2025, 102: 88.
[9] Meng Li, Yihang Guo, Jingjiang Bi, Efficient energy-stable parametric finite element methods for surface diffusion flow and applications in solid-state dewetting. Communications in Computational Physics, 2025, DOI: 10.4208/cicp.OA-2024-0157.
[10] Meng Li, Nan Wang, Ruofan Zhao, Chunjie Zhou, A sharp-interface approach for simulating solid-state dewetting of thin films with double-bubble structure. Applied Mathematical Modelling, 2025, 149: 116318.
[11] Meng Li, Dan Wang, Junjun Wang, Xiaolong Zhao, Variable-time-step weighted IMEX FEMs for nonlinear evolution equations. Applied Numerical Mathematics, 2025, 211: 123-143.
[12] Fang Chen, Meng Li*, Yanmin Zhao, Crank-Nicolson Galerkin approximations for logarithmic Klein-Gordon equation. Journal of Computational Mathematics, 2025, 3: 641-672.
[13] Lechuan Gu, Yihang Guo, Meng Li*, High-order BDFk parametric finite element methods for anisotropic surface diffusion flows and applications in solid-state dewetting. East Asian Journal on Applied Mathematics, 2025, to appear.
[14] Meng Li, Ke Wang, Nan Wang, Structure-preserving, weighted implicit-explicit schemes for multi-phase incompressible Navier-Stokes/Darcy coupled nonlocal Allen-Cahn model. Journal of Computational and Applied Mathematics, 2025, to appear.
[15] Meng Li, Jingjiang Bi, Nan Wang. Structure-preserving weighted BDF2 methods for anisotropic Cahn-Hilliard model: Uniform/variable-time-steps. Communications in Nonlinear Science and Numerical Simulation, 2025, 140: 108395.
[16] Nan Wang, Binbin Jiang, Meng Li*, A high-order energy stable method for the MBE models with slope selection by using Lagrange multiplier approach. Applied Mathematics Letters, 2025, 160: 109316.
2024
[1] Meng Li, Quan Zhao, Parametric finite element approximations for anisotropic surface diffusion with axisymmetric geometry. Journal of Computational Physics, 2024, 497: 112632.
[2] Meng Li, Jikun Zhao, Zhongchi Wang, Shaochun Chen, Conservative conforming and nonconforming VEMs for fourth order nonlinear Schrödinger equations with trapped term. Journal of Computational Mathematics, 2024, 42(2), 454-499.
[3] Meng Li, Jikun Zhao, Shaochun Chen, Unconditional error analysis of VEMs for a generalized nonlinear Schrödinger equation. Journal of Computational Mathematics, 2024, 42(2), 500-543.
[4] Huaijun Yang, Meng Li*,Unconditional superconvergence analysis of a structure-preserving finite element method for the Poisson-Nernst-Planck equations. Advances in Computational Mathematics, 2024, 50(3): 43.
[5] Xiaodi Zhang, Meng Li*, Analysis of a semi-implicit and structure- preserving finite element method for the incompressible MHD equations with magnetic- current formulation. Communications in Nonlinear Science and Numerical Simulation, 2024, 128: 107677.
[6] Zhen Guan, Meng Li*, Junjun Wang, The nonconforming virtual element method for Sobolev equations with Burger's type nonlinearity. Communications in Nonlinear Science and Numerical Simulation, 2024, 131: 107881.
[7] Wangyuan Ming, Mengting Li, Yu Lu, Meng Li*, A fast lineared Galerkin finite element method for the nonlinear multi-term time fractional wave equation. Computers & Mathematics with Applications, 2024, 157: 27-48.
[8] Lingli Wang, Meng Li*, Shanshan Peng, Conservative EQ1rot nonconforming FEM for nonlinear Schrödinger equation with wave operator. Numerical Methods for Partial Differential Equations, 2024, 40(1): 23057.
[9] Shanshan Peng, Meng Li*, Yanmin Zhao, Fawang Liu, Fangfang Cao, Unconditionally convergent and superconvergent finite element method for nonlinear time-fractional parabolic equations with distributed delay. Numerical Algorithms, 2024, 95: 1643-1714.
2023
[1] Meng Li, Yifei Li, Lifang Pei, A symmetrized parametric finite element method for simulating solid-state dewetting problems. Applied Mathematical Modelling, 2023, 121: 731-750.
[2] Meng Li, Lingli Wang, Nan Wang, Variable-time-step BDF2 nonconforming VEM for coupled Ginzburg-Landau equations. Applied Numerical Mathematics, 2023, 186: 378-410.
[3] Nan wang, Meng Li*, Unconditional error analysis of a linearized BDF2 virtual element method for nonlinear Ginzburg-Landau equation with variable time step. Communications in Nonlinear Science and Numerical Simulation, 2023, 116: 106889.
[4] Dan Wang, Meng Li*, Yu Lu, Unconditionally convergent and superconvergent analysis of second-order weighted IMEX FEMs for nonlinear Ginzburg-Landau equation. Computers & Mathematics with Applications, 2023, 146: 84-105.
[5] Shanshan Peng, Meng Li*, Yanmin Zhao, Fenling Wang, Yanhua, Shi, Convergence and superconvergence analysis for nonlinear delay reaction diffusion system with nonconforming finite element. Numerical Methods for Partial Differential Equations, 2023, 39(1): 716-743.
[6] Bei Zhang, Jikun Zhao, Meng Li, The divergence-free nonconforming virtual element method for the Navier-Stokes problem. Numerical Methods for Partial Differential Equations, 2023, 39(3): 1977-1995.
[7] Junjun Wang, Meng Li*, A new energy-stable nonconforming finite element method for Sobolev equation with Burgers’type nonlinearity. Applied Mathematics Letters, 2023, 135: 108440.
[8] Yu Lu, Meng Li*, Unconditionally convergent and superconvergent FEMs for nonlinear coupled time-fractional prey–predator problem. Computational and Applied Mathematics, 2023, 42(3): 111.
[9] Fang Chen, Meng Li*, Yanmin Zhao, Yifa Tang, Convergence and superconvergence analysis of finite element methods for nonlinear Ginzburg-Landau equation with Caputo derivative. Computational and Applied Mathematics, 2023, 42:271.
[10] Yong-Liang Zhao, Meng Li*, Full-rank and low-rank splitting methods for the Swift–Hohenberg equation. Communications in Nonlinear Science and Numerical Simulation, 2023, 127: 107532.
[11] Lifang Pei, Chaofeng Zhang, Meng Li*, Dissipative nonconforming virtual element method for the fourth order nonlinear extended Fisher-Kolmogorov equation. Computers & Mathematics with Applications, 2023, 152:28-45.
[12] Lifang Pei, Man Zhang, Meng Li*, A novel error analysis of nonconforming finite element for the clamped Kirchhoff plate with elastic unilateral obstacle. Networks and Heterogeneous Media, 2023, 18(3): 1178–1189.
2022
[1] Meng Li, Cut-off error splitting technique for conservative nonconforming VEM for N-coupled nonlinear Schrödinger-Boussinesq equations. Journal of Scientific Computing, 2022, 93:86.
[2] Meng Li, Jikun Zhao, Chengming Huang, Shaochun Chen, Conforming and nonconforming VEMs for the fourth-order reaction-subdiffusion equation: a unified framework. IMA Journal of Numerical Analysis, 2022, 42(3), 2238-2300.
[3] Lingli Wang , Meng Li*. Galerkin finite element method for damped nonlinear Schrödinger equation. Applied Numerical Mathematics, 2022, 178: 216-247.
[4] Meng Li, Yifan Wei, Binqian Niu, Yong-Liang Zhao, Fast L2-1σ Galerkin FEMs for generalized nonlinear coupled Schrödinger equations with Caputo derivatives. Applied Mathematics and Computation, 2022, 416: 126734.
[5] Junjun Wang, Meng Li*, Yu Zhang, Superconvergence analysis of BDF-Galerkin FEM for nonlinear Schrödinger equation. Numerical Algorithms, 2022, 89(1): 195-222.
[6] Zhongchi Wang, Meng Li*, Superconvergence analysis of anisotropic finite element method for the time fractional substantial diffusion equation with smooth and nonsmooth solutions. Mathematical Methods in the Applied Sciences, 2022,46(5): 5545-5560.
[7] Junjun Wang, Meng Li*, Superconvergence results for nonlinear Klein-Gordon-Schrödinger equation with backward differential formula finite element method. Computers & Mathematics with Applications, 2022,118:214-229.
2021
[1] Meng Li, Jikun Zhao, Nan Wang, Shaochun Chen, Conforming and nonconforming conservative virtual element methods for nonlinear Schrödinger equation: A unified framework. Computer Methods in Applied Mechanics and Engineering, 2021, 380: 113793.
[2] Nan Wang, Meng Li*, Chengming Huang, Unconditional energy dissipation and error estimates of the SAV fourier spectral method for nonlinear fractional generalized wave equation. Journal of Scientific Computing, 2021, 88: 19.
[3] Junjun Wang, Meng Li*, Mengping Jiang, Superconvergence analysis of a MFEM for BBM equation with a stable scheme. Computers & Mathematics with Applications, 2021, 93: 168-177.
[4] Junjun Wang, Meng Li*, Lijuan Guo, Superconvergence analysis for nonlinear Schrödinger equation with two-grid finite element method. Applied Mathematics Letters, 2021, 122: 107553.
[5] Yong-Liang Zhao, Meng Li*, Alexander Ostermann, Xian-Ming Gu, An efficient second-order energy stable BDF scheme for the space fractional Cahn-Hilliard equation. BIT Numerical Mathematics, 2021, 61(3): 1061-1092.
[6] Yong-Liang Zhao, Xian-Ming Gu, Meng Li, Huan-Yan Jian, Preconditioners for all-at-once system from the fractional mobile/immobile advection-diffusion model. Journal of Applied Mathematics and Computing, 2021, 65(1): 669-691.
2020
[1] Meng Li, Dongyang Shi, Junjun Wang, Unconditional superconvergence analysis of a linearized Crank-Nicolson Galerkin FEM for generalized Ginzburg-Landau equation. Computers & Mathematics with Applications, 2020, 79(8): 2411-2425.
[2] Meng Li, Chengming Huang, Yong-liang Zhao, Fast conservative numerical algorithm for the coupled fractional Klein-Gordon-Schrödinger equation. Numerical Algorithms, 2020, 84(3), 1081-1119.
[3] Meng Li, Nan Wang, Mingfa Fei, Chengming Huang, A dissipation-preserving finite element method for nonlinear fractional wave equations on irregular convex domains. Mathematics and Computers in Simulation, 2020, 177, 404-419.
[4] Meng Li, Dongyang Shi, Lifang Pei, Convergence and superconvergence analysis of finite element methods for the time fractional diffusion equation. Applied Numerical Mathematics, 2020, 151: 141-160.
[5] Meng Li, Chengming Huang, Wanyuan Ming, A relaxation-type Galerkin FEM for nonlinear fractional Schrödinger equations. Numerical Algorithms, 2020, 83(1): 99-124.
[6] Nan Wang, Mingfa Fei, Chengming Huang, Guoyu Zhang, Meng Li, Dissipation-preserving Galerkin-Legendre spectral methods for two-dimensional fractional nonlinear wave equations. Computers & Mathematics with Applications, 2020, 80, 617-635.
2019
[1] Meng Li, A high-order split-step finite difference method for the system of the space fractional CNLS. European Physical Journal Plus, 2019, 134:244.
[2] Meng Li, Chengming Huang, An efficient difference scheme for the coupled nonlinear fractional Ginzburg-Landau equations with the fractional Laplacian. Numerical Methods for Partial Differential Equations, 2019, 35(1), 394-421.
[3] Meng Li, Dongyang Shi, Junjun Wang, Wanyuan Ming, Unconditional superconvergence analysis of the conservative linearized Galerkin FEMs for nonlinear Klein-Gordon-Schrödinger equation. Applied Numerical Mathematics, 2019, 142: 47-63.
[4] Meng Li, Jikun Zhao, Chengming Huang, Shaochun Chen, Nonconforming virtual element method for the time fractional reaction-subdiffusion equation with non-smooth data. Journal of Scientific Computing, 2019, 81: 1823-1859.
[5] Zongbiao Zhang, Meng Li*, Wang Zhongchi, A linearized Crank-Nicolson Galerkin FEMs for the nonlinear fractional Ginzburg-Landau equation. Applicable Analysis, 2019, 98(15): 2648–2667
2018
[1] Meng Li, Xianming Gu, Chengming Huang, Mingfa Fei, Guoyu Zhang, A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations. Journal of Computational Physics, 2018, 358:256-282.
[2] Meng Li, Yong-liang Zhao, A fast energy conserving finite element method for the nonlinear fractional Schrödinger equation with wave operator. Applied Mathematics and Computation, 2018, 338(1), 758-773.
[3] Meng Li, Chengming Huang, Zongbiao Zhang, Unconditional error analysis of Galerkin FEMs for nonlinear fractional Schrödinger equation. Applicable Analysis, 2018, 97(2): 295-315.
[4] Meng Li, Chengming Huang, Wanyuan Ming, Mixed finite element method for multi-term time-fractional diffusion and diffusion-wave equations. Computational and Applied Mathematics, 2018, 37(2), 2309–2334.
[5] Guoyu Zhang, Chengming Huang, Meng Li, A mass-energy preserving Galerkin FEM for the coupled nonlinear fractional Schrödinger equations. European Physical Journal Plus, 2018, 133(4): 155.
2016-2017
[1] Meng Li, Chengming Huang, Pengde Wang, Galerkin finite element method for nonlinear fractional Schrödinger equations. Numerical Algorithms, 2017, 74(2): 499-525.
[2] Meng Li, Chengming Huang, Nan Wang, Galerkin finite element method for nonlinear fractional Ginzburg-Landau equation. Applied Numerical Mathematics, 2017, 118: 131-149.
[3] Meng Li, Chengming Huang, ADI Galerkin FEMs for the 2D nonlinear time-space fractional diffusion-wave equation. International Journal of Modeling, Simulation, and Scientific Computing, 2017, 1750025.
[4] Meng Li, Chengming Huang, Fengze Jiang, Galerkin finite element method for higher dimensional multi-term fractional diffusion equation on non-uniform meshes. Applicable Analysis, 2017, 96(8): 1269-1284.
[5] Wanyuan Ming, Chengming Huang, Meng Li, Superconvergence in collocation methods for Volterra integral equations with vanishing delays. Journal of Computational & Applied Mathematics, 2016, 308: 361-378.
举办会议、参加国内外会议、组织专题
1. 可计算建模、仿真与应用青年研讨会，华中科技大学，2025.05.16-2025.05.19；
2. 科学计算及其应用研讨会，北京师范大学，2025.05.09-2025.05.11；
3. 偏微分方程数值解研讨会，中国科技大学，2025.04.12-2025.04.13；
4. 第14届AIMS会议, New York University（Abu Dhabi UAE）, ss30：Recent Development in Advanced Numerical Methods for Partial Differential Equations, 2024.12.16-2024.12.21；
5. 虚拟元方法的理论和应用研讨会，湘潭大学，2024.11.08-2024.11.11；
6. 中国工业与应用数学学会第二十二届年会（CSIAM 2024），专题“TM36：量子力学中的数学模型，2024.10.24-2024.10.27；
7. “第十一届全国青年计算物理学术会议”，内蒙古呼和浩特，2024.08.12-2024.08.14；
8. 界面问题: 建模、分析、计算及应用研讨会，国家天元数学东北中心，2024.08.13-2024.08.18；
9. International Conference on Scientific Computation and Differential Equations, National University of Singapore, Mathematical Modeling, Analysis and numerical methods for interface problems and related geometric flows, 2024.07.15-2024.07.19；
10. Numerical methods for fractional-derivative problems, 北京计算科学研究中心, 2024.07.08-2024.07；
11. 科学工程计算中的数值和机器学习方法研讨会, 西北工业大学,2024.05.31-2024.06.02；
12. 2024科学计算及应用前沿研讨会, 新疆大学, 2024.05.12-2024.05.14；
13. 2024年微分方程数值方法及其应用青年学术研讨会,湘潭大学举办,2024.04.19-2024.04.21；
14. 半导体器件多物理场建模与仿真研讨会, 天元数学国际交流中心（昆明）, 2024.03.31- 2024.04.06；
15. 半导体器件多物理场建模与仿真, 北京, 2024.01.19-2024.01.21;
16. 多物理场与复杂系统计算前沿研讨会, 郑州, 2023.11.24-2023.11.26；
17. 第五届“International Workshop on Numerical Analysis and Applications of Fractional Differential Equations”，哈工大（深圳）, 专题：“Numerical Methods and Applications for some nonlocal Models”, 2023.11.10-2023.11.13；
18. 全国计算物理会议, 北京, 2023.10.22-2023.10.26；
19. 中国仿真学会仿真算法专业委员会, 新疆伊犁, 2023.08.01-2023.08.05；
20. 第十三届中国数学会计算数学年会, 南京, 专题：“分数阶微分方程的数值解法”, 2023.07.15-2023.07.19。
