Two-grid virtual element discretization of semilinear elliptic problem

被引：3
|
作者：
Chen, Fengxin [1 ]
Wang, Qiming [2 ]
Zhou, Zhaojie [3 ]
机构：
[1] Shandong Jiaotong Univ, Sch Sci, Jinan, Peoples R China
[2] Beijing Normal Univ, Sch Math Sci, Beijing, Peoples R China
[3] Shandong Normal Univ, Sch Math & Stat, Jinan, Peoples R China
来源：
APPLIED NUMERICAL MATHEMATICS | 2023年 / 186卷
关键词：
Virtual element method; Two grid algorithm; A priori error estimate; STOKES PROBLEM;
D O I：
10.1016/j.apnum.2023.01.009
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper a two grid algorithm for semilinear elliptic problem based on virtual element method (VEM) discretization is proposed. With this new algorithm the solution of a semilinear elliptic problem on a fine grid is reduced to the solution of a semilinear elliptic problem on a much coarser grid, and the solution of a linear system on the fine grid. A priori error estimates in H1 and L2 norms are derived. Numerical experiments are carried out to illustrate the theoretical findings.(c) 2023 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：228 / 240
页数：13
相关论文
共 50 条
  • [1] Two-Grid Virtual Element Discretization of Quasilinear Elliptic Problem
    Chen, Fengxin
    Yang, Minghui
    Zhou, Zhaojie
    MATHEMATICAL MODELLING AND ANALYSIS, 2024, 29 (01) : 77 - 89
  • [2] A two-grid discretization scheme for semilinear elliptic eigenvalue problems
    Chien, CS
    Jeng, BW
    SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2006, 27 (04): : 1287 - 1304
  • [3] Iterative two-grid methods for discontinuous Galerkin finite element approximations of semilinear elliptic problem
    Zhan, Jiajun
    Zhong, Liuqiang
    Peng, Jie
    ADVANCES IN COMPUTATIONAL MATHEMATICS, 2023, 49 (06)
  • [4] Iterative two-grid methods for discontinuous Galerkin finite element approximations of semilinear elliptic problem
    Jiajun Zhan
    Liuqiang Zhong
    Jie Peng
    Advances in Computational Mathematics, 2023, 49
  • [5] A two-grid stabilized mixed finite element method for semilinear elliptic equations
    Weng, Zhifeng
    Feng, Xinlong
    Liu, Demin
    APPLIED MATHEMATICAL MODELLING, 2013, 37 (10-11) : 7037 - 7046
  • [6] Iterative two-grid methods for semilinear elliptic equations
    Zhang, Weifeng
    Fan, Ronghong
    Zhong, Liuqiang
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2020, 80 (03) : 522 - 530
  • [7] Analysis of two-grid discretization scheme for semilinear hyperbolic equations by mixed finite element methods
    Wang, Keyan
    Chen, Yanping
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (09) : 3370 - 3391
  • [8] Two-grid IPDG discretization scheme for nonlinear elliptic PDEs
    Zhong, Liuqiang
    Zhou, Liangliang
    Liu, Chunmei
    Peng, Jie
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2021, 95
  • [9] A two-grid discretization scheme for the Steklov eigenvalue problem
    Li Q.
    Yang Y.
    Journal of Applied Mathematics and Computing, 2011, 36 (1-2) : 129 - 139
  • [10] Two-grid weak Galerkin method for semilinear elliptic differential equations
    Chen, Luoping
    Wu, Fanyun
    Zeng, Guoyan
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (01) : 423 - 437
12345