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Moving Finite Element Simulations for Reaction-Diffusion Systems

Published online by Cambridge University Press:  03 June 2015

Guanghui Hu ,
Zhonghua Qiao  and
Tao Tang
Guanghui Hu*
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027, USA
Zhonghua Qiao*
Affiliation:
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
Tao Tang*
Affiliation:
Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
*
URL:myweb.polyu.edu.hk/∼zqiao/, Email: ghhu@math.msu.edu
Corresponding author. Email: zqiao@inet.polyu.edu.hk
Email: ttang@math.hkbu.edu.hk
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Abstract

This work is concerned with the numerical simulations for two reaction-diffusion systems, i.e., the Brusselator model and the Gray-Scott model. The numerical algorithm is based upon a moving finite element method which helps to resolve large solution gradients. High quality meshes are obtained for both the spot replication and the moving wave along boundaries by using proper monitor functions. Unlike [33], this work finds out the importance of the boundary grid redistribution which is particularly important for a class of problems for the Brusselator model. Several ways for verifying the quality of the numerical solutions are also proposed, which may be of important use for comparisons.

Keywords

65M5065M60Reaction-diffusion systemsBrusselator modelGray-Scott modelmoving finite element method
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 3 , June 2012 , pp. 365 - 381
Copyright
Copyright © Global-Science Press 2012

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