IMPLICIT-EXPLICIT TIMESTEPPING WITH FINITE ELEMENT APPROXIMATION OF REACTION-DIFFUSION SYSTEMS ON EVOLVING DOMAINS

Omar Lakkis*, Anotida Madzvamuse, Chandrasekhar Venkataraman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)

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-infinity(0, T; L-2(Omega)) and L-2(0, T; H-1(Omega)) 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.

Original languageEnglish
Pages (from-to)2309-2330
Number of pages22
JournalSiam journal on numerical analysis
Volume51
Issue number4
DOIs
Publication statusPublished - 2013

Keywords

  • evolving domain
  • implicit-explicit scheme
  • finite element method
  • convergence rate
  • Eulerian scheme
  • Lagrangian scheme
  • PATTERN-FORMATION
  • PARABOLIC EQUATIONS
  • DIFFERENCE METHODS
  • GROWING DOMAINS
  • STABILITY
  • CONVERGENCE
  • DISCRETE
  • SYMMETRY
  • GROWTH
  • MODEL

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