LakkisMadzvamuseVenkataraman-2013-A-article-Implicit--Explicit.pdf (586.7 kB)
Implicit-explicit timestepping with finite element approximation of reaction-diffusion systems on evolving domains
journal contribution
posted on 2023-06-08, 23:32 authored by Omar LakkisOmar Lakkis, Anotida MadzvamuseAnotida Madzvamuse, Chandrasekhar VenkataramanChandrasekhar VenkataramanWe 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.
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- Published
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- Published version
Journal
SIAM Journal on Numerical AnalysisISSN
0036-1429Publisher
Society for Industrial and Applied MathematicsExternal DOI
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4Volume
51Page range
2309-2330Department affiliated with
- Mathematics Publications
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- Yes
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- Yes
Legacy Posted Date
2015-11-24First Open Access (FOA) Date
2015-11-24First Compliant Deposit (FCD) Date
2015-11-24Usage metrics
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