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

页数：13

共 50 条

[1] TWO-GRID ALGORITHM OF H1-GALERKIN MIXED FINITE ELEMENT METHODS FOR SEMILINEAR PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS
Hou, Tianliang
Liu, Chunmei
Dai, Chunlei
Chen, Luoping
Yang, Yin
[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS, 2022, 40 (05) : 671 - 689
[2] SUPERCLOSE ANALYSIS OF A TWO-GRID FINITE ELEMENT SCHEME FOR SEMILINEAR PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS
Xu, Changling
Hou, Tianliang
[J]. ELECTRONIC RESEARCH ARCHIVE, 2020, 28 (02): : 897 - 910
[3] Two-grid H1-Galerkin mixed finite elements combined with L1 scheme for nonlinear time fractional parabolic equations
Pan, Jun
Tang, Yuelong
[J]. ELECTRONIC RESEARCH ARCHIVE, 2023, 31 (12): : 7207 - 7223
[4] Analysis of two-grid discretization scheme for semilinear hyperbolic equations by mixed finite element methods
Wang, Keyan
Chen, Yanping
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (09) : 3370 - 3391
[5] Analysis of Two-Grid Methods for Nonlinear Parabolic Equations by Expanded Mixed Finite Element Methods
Chen, Yanping
Luan, Peng
Lu, Zuliang
[J]. ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2009, 1 (06) : 830 - 844
[6] Two-Grid Finite Volume Element Method Combined with Crank-Nicolson Scheme for Semilinear Parabolic Equations
Lou, Yuzhi
Chen, Chuanjun
Xue, Guanyu
[J]. ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2021, 13 (04) : 892 - 913
[7] Two-grid scheme of expanded mixed finite element method for semilinear parabolic integro-differential equations
Hou, Tianliang
Jiang, Wenzhu
Chen, Luoping
[J]. APPLICABLE ANALYSIS, 2022, 101 (08) : 3017 - 3038
[8] Superconvergence of H1-Galerkin mixed finite element methods for parabolic problems
Tripathy, Madhusmita
Sinha, Rajen K.
[J]. APPLICABLE ANALYSIS, 2009, 88 (08) : 1213 - 1231
[9] H1-Galerkin mixed finite element methods for parabolic partial integro-differential equations
Pani, AK
Fairweather, G
[J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 2002, 22 (02) : 231 - 252
[10] Two-Grid Methods for a New Mixed Finite Element Approximation of Semilinear Parabolic Integro-Differential Equations
Liu, C.
Hou, T.
[J]. NUMERICAL ANALYSIS AND APPLICATIONS, 2019, 12 (02) : 137 - 154

← 1 2 3 4 5 →