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

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 correspondi...

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Bibliographic Details
Published inInternational journal of computer mathematics Vol. 96; no. 10; pp. 2010 - 2023
Main Authors Chen, Chuanjun, Zhang, Xiaoyan, Zhang, Guodong, Zhang, Yuanyuan
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 03.10.2019
Taylor & Francis Ltd
Subjects
Differential equations
error estimates
Finite element analysis
Finite element method
Mathematical analysis
Nonlinear equations
nonlinear parabolic integro-differential equations
Nonlinear programming
Nonlinear systems
Two-grid
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ISSN0020-7160
1029-0265
DOI10.1080/00207160.2018.1548699

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Summary: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.
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ISSN:0020-7160
1029-0265
DOI:10.1080/00207160.2018.1548699