Finite Element Simulations with Adaptively Moving Mesh for the Reaction Diffusion System

A moving mesh method is proposed for solving reaction-diffusion equations. The finite element method is used to solving the partial different equation system, and an efficient numerical scheme is applied to implement mesh moving. In the practical calculations, the moving mesh step and the problem eq...

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Bibliographic Details
Published inNumerical Mathematics: Theory, Methods and Applications Vol. 9; no. 4; pp. 686 - 704
Main Authors Xie, Congcong, Hu, Xianliang
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.11.2016
Subjects
reaction-diffusion
growing domain
65N50
65M60
moving mesh
pattern formation
finite elements
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ISSN1004-8979
2079-7338
DOI10.4208/nmtma.2016.m1229

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Summary:A moving mesh method is proposed for solving reaction-diffusion equations. The finite element method is used to solving the partial different equation system, and an efficient numerical scheme is applied to implement mesh moving. In the practical calculations, the moving mesh step and the problem equation solver are performed alternatively. Several numerical examples are presented, including the Gray-Scott, the Activator-Inhibitor and a case with a growing domain. It is illustrated numerically that the moving mesh methods costs much lower, compared with the numerical schemes on a fixed mesh. Even in the case of complex pattern dynamics described by the reaction-diffusion systems, the adapted meshes can capture the details successfully.
ISSN:1004-8979
2079-7338
DOI:10.4208/nmtma.2016.m1229