Numerical analysis for a system coupling curve evolution attached orthogonally to a fixed boundary, to a reaction–diffusion equation on the curve
Vanessa Styles, James Van Yperen · Numerical Methods for Partial Differential Equations · 2021
Abstract We consider a semidiscrete 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 , such that the curve meets the boundary orthogonally, and the forcing is a function of the solution of a reaction–diffusion equation that holds on the evolving curve. We prove optimal order error bounds for the resulting approximation and present numerical experiments.