姓名：李猛
职务/职称：硕士生导师/副教授
研究领域：虚拟元方法、有限元方法、谱方法以及配置方法，目前主要研究非线性（局部及非局部）模型、几何偏微分方程的保结构算法、快速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月至今在郑州大学数学与统计学院工作；
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，主持；
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，主持;
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，主持;
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，主持;
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，在研，合作项目
奖励
1.河南省自然科学奖二等奖，河南省人民政府;
2.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）;
3.河南省优秀学位论文指导教师;
4.博士研究生国家奖学金;
5.华中科技大学优秀毕业研究生
其他
目前担任中国计算物理学会理事
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
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]Xiaodi Zhang,Meng Li*,Analysis of a semi-implicit and structure- preserving finite element method for theincompressible MHD equations with magnetic- current formulation. Communications in Nonlinear Science and Numerical Simulation, 2024, 128: 107677.
[5]Fang Chen,Meng Li*, Yanmin Zhao, Crank-NicolsonGalerkinApproximationsforlogarithmic Klein-Gordon equation.Journal of Computational Mathematics,2024,To appear.
[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 and Mathematics with Applications, 2024, 157: 27-48.
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-orderweighted 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]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.
[7]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.
[8]Lingli Wang,Meng Li*,Shanshan Peng,ConservativeEQ1rotnonconforming FEM for nonlinear Schrödinger equation withwave operator.Numerical Methods for Partial Differential Equations,2023, DOI: 10.1002/num.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, 2023, DOI: 10.1007/s11075-023-01624-8.
[10]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.
[11]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.
[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.
[13]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.
[14]Lifang Pei,ChaofengZhang,Meng Li*,Dissipative nonconforming virtual element method for the fourth order nonlinear extended Fisher-Kolmogorov equation.Computers & Mathematics with Applications,2023, 152:28-45.
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 and 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 and 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 and 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 and 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. The European Physical Journal Plus, 2019, 134:244.
[2] 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
[3]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.
[4]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.
[5]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.
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 & 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.
