研究方向：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。

个人简介：郑州大学副教授，理学博士，硕士研究生导师。2017.7毕业于华中科技大学数学与统计学院，2017.7入职郑州大学，2018.1入站博士后，2022.8-2023.8新加坡国立大学访问学者。主要研究方向为偏微分方程数值解，在IMA Journal of Numerical Analysis, Computer Methods in Applied Mechanics and Engineering, Journal of Computational Physics, Journal of Scientific Computing, BIT Numerical Mathematics, Journal of Computational Mathematics, Applied Mathematical Modelling等发表学术论文五十余篇，多篇入选ESI高被引论文，总引用次数：860。主持中国博士后科学基金特别资助项目（站中）、国家自然科学基金青年项目、中国博士后面上项目、河南省高等学校重点科研项目等。曾获河南省自然科学奖二等奖、河南省优秀科技论文一等奖等。

讲授课程：数值分析、微积分

科研成果：

主持或参加科研项目（课题）情况

1. 中国博士后科学基金第16批特别资助 (站中)，2023T160589, 2023/01-，主持；

2. 国家自然科学基金青年项目，11801527，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，2018M632791，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，19A110034，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，1191101330，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;

6. 国家自然科学基金面上项目，11771163，几类带非局部特征刚性问题的高效数值算法及其理论分析，2018/01-2021/12，参与。

代表性研究成果和学术奖励

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。

科研论文（2016-）

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] 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, 2023,DOI:10.4208/jcm.2209-m20 21-0038.

[4] Meng Li, Jikun Zhao, Shaochun Chen, Unconditional error analysis of VEMs for a generalized nonlinear Schrödinger equation. Journal of Computational Mathematics, 2023, DOI:10.4208/jcm. 2207-m2022-0055.

[5] 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.

[6] 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.

[7] 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.

[8] 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.

[9] 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.

[10] Lingli Wang, Meng Li*, Shanshan Peng, Conservative EQ1rot nonconforming FEM for nonlinear Schrödinger equation with wave operator. Numerical Methods for Partial Differential Equations, 2023, DOI: 10.1002/num.23057.

[11] 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.

[12] 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.

[13] 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.

[14] 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 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.

教学成果：

牛彬倩2020届本科生：河南省优秀毕业论文.

所带学生取得的成果：

1. 王玲丽2023届硕士研究生：国家奖学金、河南省优秀毕业生、郑州大学优秀毕业生、郑州大学三好研究生；

2. 彭杉杉2023届硕士研究生：郑州大学三好研究生、郑州大学蜜雪冰城奖学金.