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

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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 L8(0, T; L2(O)) and L2(0, T; H1(O)) 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.

History

Publication status

  • Published

File Version

  • Published version

Journal

SIAM Journal on Numerical Analysis

ISSN

0036-1429

Publisher

Society for Industrial and Applied Mathematics

Issue

4

Volume

51

Page range

2309-2330

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2015-11-24

First Open Access (FOA) Date

2015-11-24

First Compliant Deposit (FCD) Date

2015-11-24

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