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

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 $\Omega\subset \mathbb{R}^2$ and meets $\partial \Omega$ 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.