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

[img] PDF (© 2013, Society for Industrial and Applied Mathematics) - Published Version
Download (600kB)

Abstract

We present and analyze an implicit–explicit timestepping procedure with finite element
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 introduces
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: Chandrasekhar Venkataraman
Date Deposited: 24 Nov 2015 13:41
Last Modified: 07 Mar 2017 03:54
URI: http://sro.sussex.ac.uk/id/eprint/58457

View download statistics for this item

📧 Request an update