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Two-Grid Discretization Scheme for Nonlinear Reaction Diffusion Equation by Mixed Finite Element Methods

Published online by Cambridge University Press:  03 June 2015

Luoping Chen  and
Yanping Chen
Luoping Chen*
Affiliation:
School of Mathematic, Southwest Jiaotong University, Chengdu 611756, P.R. China
Yanping Chen*
Affiliation:
School of Mathematic science, South China Normal University, Guangzhou 510631, P.R. China
*
Email: clpchenluoping@163.com
Corresponding author. Email: yanpingchen@scnu.edu.cn
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Abstract

In this paper, we study an efficient scheme for nonlinear reaction-diffusion equations discretized by mixed finite element methods. We mainly concern the case when pressure coefficients and source terms are nonlinear. To linearize the nonlinear mixed equations, we use the two-grid algorithm. We first solve the nonlinear equations on the coarse grid, then, on the fine mesh, we solve a linearized problem using Newton iteration once. It is shown that the algorithm can achieve asymptotically optimal approximation as long as the mesh sizes satisfy H = O(h1/2). As a result, solving such a large class of nonlinear equations will not be much more difficult than getting solutions of one linearized system.

Keywords

65M1265M1565M60Two-grid methodreaction-diffusion equationsmixed finite element methods
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 2 , April 2014 , pp. 203 - 219
Copyright
Copyright © Global-Science Press 2014

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