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

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• 作者：Anotida Madzvamuse
• 关键词：Implicit– ; explicit schemes ; Time-stepping methods ; Finite elements ; Moving meshes ; Moving grid finite elements ; Reaction– ; diffusion systems ; Schnakenberg model
• 刊名：Journal of Computational Physics
• 出版年：2006
• 出版时间：1 May 2006
• 年：2006
• 卷：214
• 期：1
• 页码：239-263
• 全文大小：4459 K

文摘

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.