Finite element approximation of a system coupling curve evolution with prescribed normal contact to a fixed boundary to reaction-diffusion on the curve

2020/02/27 by Styles, Vanessa, Van Yperen, James
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2002.11996

Abstract

We consider a finite element approximation for a system consisting of the evolution of a curve evolving by forced curve shortening flow coupled to a reaction-diffusion equation on the evolving curve. The curve evolves inside a given domain Ω⊂ ℝ² and meets ∂ Ω orthogonally. The scheme for the coupled system is based on the schemes derived in [BDS17] and [DE98]. We present numerical experiments and show the experimental order of convergence of the approximation.

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