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

02/27/2020

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by   Vanessa Styles, et al.

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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⊂R^2 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.