  We consider a semi-discrete finite element approximation for a system
consisting of the evolution of a planar curve evolving by forced curve
shortening flow inside a given bounded domain $\Omega \subset \mathbb{R}^2$,
such that the curve meets the boundary $\partial \Omega$ orthogonally, and the
forcing is a function of the solution of a reaction-diffusion equation that
holds on the evolving curve. We prove optimal error bounds for the resulting
approximation and present numerical experiments.
