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

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 O?R2 and meets ??O orthogonally. We present numerical experiments and show the experimental order of convergence of the approximation.