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

Numerical analysis for a system coupling curve evolution attached orthogonally to a fixed boundary, to a reaction-diffusion equation on the curve