A two-grid finite element method for nonlinear parabolic integro-differential equations

被引：51

作者：

Chen, Chuanjun ^{[1
]}

Zhang, Xiaoyan ^{[1
]}

Zhang, Guodong ^{[1
]}

Zhang, Yuanyuan ^{[1
]}

机构：

[1] Yantai Univ, Sch Math & Informat Sci, Yantai 264005, Peoples R China

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2019年 / 96卷 / 10期

基金：

中国国家自然科学基金;

关键词：

Two-grid; nonlinear parabolic integro-differential equations; finite element method; error estimates; MISCIBLE DISPLACEMENT PROBLEM; EVOLVING SCALES;

D O I：

10.1080/00207160.2018.1548699

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a two-grid finite element method (FEM) for a two-dimensional nonlinear parabolic integro-differential equation. We solve a fully nonlinear system on a coarse grid space with a grid size H and derive a rough approximation of the exact solution, and then solve the corresponding linearized problem on a fine grid space with a grid size h. The optimal error estimates in -norm are obtained for spatially the semidiscrete two-grid FEM. Finally, numerical examples are given to testify the efficiency of the method.

引用

页码：2010 / 2023

页数：14

共 38 条

[1] Backward solutions to nonlinear integro-differential systems [J].

Bai, Yuzhen .

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2010, 8 (04) :807-815

[2]

Brunner H., 1982, J COMPUT APPL MATH, V8, P213, DOI [DOI 10.1016/0771-050X(82)90044-4, 10.1016/0771-050X(82)90044-4]

[3]

Cannon J. R., 1988, Calcolo, V25, P187, DOI 10.1007/BF02575943

[4] A PRIORI L2 ERROR-ESTIMATES FOR FINITE-ELEMENT METHODS FOR NONLINEAR DIFFUSION-EQUATIONS WITH MEMORY [J].

CANNON, JR ;

LIN, YP .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1990, 27 (03) :595-607

[5] Two-Grid Method for Nonlinear Reaction-Diffusion Equations by Mixed Finite Element Methods [J].

Chen, Luoping ;

Chen, Yanping .

JOURNAL OF SCIENTIFIC COMPUTING, 2011, 49 (03) :383-401

[6]

Chen Y. F, 2016, EVID-BASED COMPL ALT, V1, P1

[7] Two-Grid Method for Miscible Displacement Problem by Mixed Finite Element Methods and Mixed Finite Element Method of Characteristics [J].

Chen, Yanping ;

Hu, Hanzhang .

COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2016, 19 (05) :1503-1528

[8] Two-Grid method for nonlinear parabolic equations by expanded mixed finite element methods [J].

Chen, Yanping ;

Chen, Luoping ;

Zhang, Xiaochun .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2013, 29 (04) :1238-1256

[9] A two-grid method for expanded mixed finite-element solution of semilinear reaction-diffusion equations [J].

Chen, YP ;

Huang, YQ ;

Yu, DH .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2003, 57 (02) :193-209

[10] NONLOCAL DISPERSION IN MEDIA WITH CONTINUOUSLY EVOLVING SCALES OF HETEROGENEITY [J].

CUSHMAN, JH ;

GINN, TR .

TRANSPORT IN POROUS MEDIA, 1993, 13 (01) :123-138

← 1 2 3 4 →