Implicit--explicit timestepping with finite element approximation of reaction--diffusion systems on evolving domains

Lakkis, Omar, Madzvamuse, Anotida and Venkataraman, Chandrasekhar (2013) Implicit--explicit timestepping with finite element approximation of reaction--diffusion systems on evolving domains. SIAM Journal on Numerical Analysis, 51 (4). pp. 2309-2330. ISSN 0036-1429

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Abstract

We present and analyze an implicit–explicit timestepping procedure with finite el- ement spatial approximation for semilinear reaction–diffusion systems on evolving domains arising from biological models, such as Schnakenberg’s (1979). We employ a Lagrangian formulation of the model equations which permits the error analysis for parabolic equations on a fixed domain but intro- duces technical difficulties, foremost the space-time dependent conductivity and diffusion. We prove optimal-order error estimates in the L∞(0,T;L2(Ω)) and L2(0,T;H1(Ω)) norms, and a pointwise stability result. We remark that these apply to Eulerian solutions. Details on the implementation of the Lagrangian and the Eulerian scheme are provided. We also report on a numerical experiment for an application to pattern formation on an evolving domain.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0297 Numerical analysis
Depositing User: Omar Lakkis
Date Deposited: 19 Sep 2013 08:23
Last Modified: 15 Mar 2017 01:11
URI: http://sro.sussex.ac.uk/id/eprint/46358

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