李猛(鄭州大學數學與統計學院副教授)

研究方向：虛擬元方法、有限元方法、譜方法以及配置方法，目前主要研究非線性（局部及非局部）模型、幾何偏微分方程的保結構算法、快速算法以及機器學習等。

科研論文（2016-）

2023

[1] 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.

[2] 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.

[3] Meng Li, Lingli Wang, Nan Wang, Variable-time-step BDF2 nonconforming VEM for coupled Ginzburg-Landau equations, Applied Numerical Mathematics, 2023, To appear.

[4] 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 Equations for Partial Differential Equations, 2023, 39(1): 716-743.

[5] 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, To appear.

[6] Meng Li, Jikun Zhao, Shaochun Chen, Unconditional error analysis of VEMs for a generalized nonlinear Schrödinger equation. Journal of Computational Mathematics, 2023, To appear.

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, DOI: 10.1002/mma.8850.

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] Bei Zhang, Jikun Zhao, Meng Li, The divergence-free nonconforming virtual element method for the Navier–Stokes problem. Numerical Methods for Partial Differential Equations, 2021, DOI: 10.1002/num.22812.

[5] Junjun Wang, Meng Li*, Lijuan Guo, Superconvergence analysis for nonlinear Schrödinger equation with two-grid finite element method. Applied Mathematics Letters, 2021, 122: 107553.

[6] 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.

[7] 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.

李猛(鄭州大學數學與統計學院副教授)

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