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

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Partial differential equations, boundary value problems

Published online by Cambridge University Press:  17 November 2016

Congcong Xie  and
Xianliang Hu
Congcong Xie*
Affiliation:
College of Science, Zhejiang University of Technology, Hangzhou 310023, China
Xianliang Hu*
Affiliation:
School of Mathematical Science, Zhejiang University, Hangzhou 310027, China
*
*Corresponding author. Email addresses:xlhu@zju.edu.cn (X. Hu), ccxie@zjut.edu.cn (C. Xie)
*Corresponding author. Email addresses:xlhu@zju.edu.cn (X. Hu), ccxie@zjut.edu.cn (C. Xie)
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Abstract

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.

Keywords

moving meshfinite elementsreaction-diffusiongrowing domainpattern formation

MSC classification

Secondary: 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65N50: Mesh generation and refinement
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 9 , Issue 4 , November 2016 , pp. 686 - 704
Copyright
Copyright © Global-Science Press 2016 

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