  We consider a finite element approximation for a system consisting of the
evolution of a closed planar curve by forced curve shortening flow coupled to a
reaction-diffusion equation on the evolving curve. The scheme for the curve
evolution is based on a parametric description allowing for tangential motion,
whereas the discretisation for the PDE on the curve uses an idea from [6]. We
prove optimal error bounds for the resulting fully discrete approximation and
present numerical experiments. These confirm our estimates and also illustrate
the advantage of the tangential motion of the mesh points in practice.
