A New Two-Grid Method for Expanded Mixed Finite Element Solution of Nonlinear Reaction Diffusion Equations
Year: 2017
Author: Shang Liu, Yanping Chen
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 3 : pp. 757–774
Abstract
In the paper, we present an efficient two-grid method for the approximation of two-dimensional nonlinear reaction-diffusion equations using an expanded mixed finite-element method. We transfer the nonlinear reaction diffusion equation into first order nonlinear equations. The solution of the nonlinear system on the fine space is reduced to the solutions of two small (one linear and one non-linear) systems on the coarse space and a linear system on the fine space. Moreover, we obtain the error estimation for the two-grid algorithm. It is showed that coarse space can be extremely coarse and achieve asymptotically optimal approximation as long as the mesh sizes satisfy $h^{k+1}=\mathcal{O}(H^{3k+1})$. A numerical example is also given to illustrate the effectiveness of the algorithm.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2015.m1370
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 3 : pp. 757–774
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Error estimation mixed finite elements reaction-diffusion equations two-grid methods.
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