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We consider a finite element approximation for a system consisting of theevolution of a curve evolving by forced curve shortening flow coupled to areaction-diffusion equation on the evolving curve. The curve evolves inside agiven domain $\Omega\subset \mathbb{R}^2$ and meets $\partial \Omega$orthogonally. The scheme for the coupled system is based on the schemes derivedin [BDS17] and [DE98]. We present numerical experiments and show theexperimental order of convergence of the approximation.

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