SUPERCLOSE ANALYSIS OF H1-GALERKIN MIXED FINITE ELEMENT METHODS COMBINED WITH TWO-GRID SCHEME FOR SEMILINEAR PARABOLIC EQUATIONS

被引：0
|
作者：
Zhou, Liping [1 ]
Wei, Meina [2 ]
机构：
[1] Hunan Univ Sci & Engn, Coll Sci, Yongzhou 425199, Hunan, Peoples R China
[2] Beihua Univ, Sch Math & Stat, Jilin 132013, Jilin, Peoples R China
来源：
JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS | 2023年 / 2023卷
关键词：
Crank-Nicolson scheme; Mixed finite element; Semilinear parabolic equations; Superclose; Two-grid; CRANK-NICOLSON SCHEME;
D O I：
10.23952/jnfa.2023.3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate a two-grid scheme for semilinear parabolic equations discretized by H1- Galerkin mixed finite element method combined with Crank-Nicolson scheme. Based on the interpolation and duality argument technique, we discuss superclose properties for two-grid method and H1-Galerkin mixed finite element method. The interpolation theory plays an important role in convergence analysis. Theoretical results demonstrate that the two methods have the same convergence order by choosing h = H2. Finally, a numerical example is given to verify the theoretical results.
引用
收藏
页数：13
相关论文
共 50 条
  • [21] 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
  • [22] Two-grid Raviart-Thomas mixed finite element methods combined with Crank-Nicolson scheme for a class of nonlinear parabolic equations
    Tianliang Hou
    Luoping Chen
    Yueting Yang
    Yin Yang
    Advances in Computational Mathematics, 2020, 46
  • [23] Two-grid Raviart-Thomas mixed finite element methods combined with Crank-Nicolson scheme for a class of nonlinear parabolic equations
    Hou, Tianliang
    Chen, Luoping
    Yang, Yueting
    Yang, Yin
    ADVANCES IN COMPUTATIONAL MATHEMATICS, 2020, 46 (02)
  • [24] Domain decomposition procedures combined with H1-Galerkin mixed finite element method for parabolic equation
    Sun, Tongjun
    Ma, Keying
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2014, 267 : 33 - 48
  • [25] Two-grid P02-P1 mixed finite element methods combined with Crank-Nicolson scheme for a class of nonlinear parabolic equations
    Hou, Tianliang
    Jiang, Wenzhu
    Yang, Yueting
    Leng, Haitao
    APPLIED NUMERICAL MATHEMATICS, 2019, 137 : 136 - 150
  • [26] Superconvergence analysis of an H1-Galerkin mixed finite element method for Sobolev equations
    Shi, Dongyang
    Wang, Junjun
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2016, 72 (06) : 1590 - 1602
  • [27] Fully Discrete H1-Galerkin Mixed Finite Element Methods for Parabolic Optimal Control Problems
    Hou, Tianliang
    Liu, Chunmei
    Chen, Hongbo
    NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2019, 12 (01) : 134 - 153
  • [28] H1-Galerkin expanded mixed finite element methods for nonlinear pseudo-parabolic integro-differential equations
    Che, Haitao
    Zhou, Zhaojie
    Jiang, Ziwen
    Wang, Yiju
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2013, 29 (03) : 799 - 817
  • [29] Two-grid methods for finite volume element approximations of nonlinear parabolic equations
    Chen, Chuanjun
    Yang, Min
    Bi, Chunjia
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 228 (01) : 123 - 132
  • [30] 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
12345