A numerical scheme for axisymmetric solutions of curvature-driven free boundary problems, with applications to the Willmore flow

Abstract

We present a numerical scheme for axisymmetric solutions to curvature-driven moving boundary problems governed by a local law of motion, e.g. the mean curvature flow, the surface diffusion flow, and the Willmore flow. We then present several numerical experiments for the Willmore flow. In particular, we provide numerical evidence that the Willmore flow can develop singularities in finite time.