Time-stepping schemes for moving grid finite elements applied to reaction-diffusion systems on fixed and growing domains

Madzvamuse, Anotida (2006) Time-stepping schemes for moving grid finite elements applied to reaction-diffusion systems on fixed and growing domains. Journal of Computational Physics, 214 (1). 239 - 263. ISSN 0021-9991

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Abstract

In this paper, we illustrate the application of time-stepping schemes to reaction-diffusion systems on fixed and continuously growing domains by use of finite element and moving grid finite element methods. We present two schemes for our studies, namely a first-order backward Euler finite differentiation formula coupled with a special form of linearisation of the nonlinear reaction terms (1-SBEM) and a second-order semi-implicit backward finite differentiation formula (2-SBDF) with no linearisation of the reaction terms. Our results conclude that for the type of reaction-diffusion systems considered in this paper, the 1-SBEM is more stable than the 2-SBDF scheme and that the 1-SBEM scheme has a larger region of stability (at least by a factor of 10) than that of the 2-SBDF scheme. As a result, the 1-SBEM scheme becomes a natural choice when solving reaction-diffusion problems on continuously deforming domains.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Anotida Madzvamuse
Date Deposited: 06 Feb 2012 20:43
Last Modified: 10 Jul 2012 11:32
URI: http://sro.sussex.ac.uk/id/eprint/27685
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