Error Analysis for a Finite Difference Scheme for Axisymmetric Mean Curvature Flow of Genus-0 Surfaces

We consider a finite difference approximation of mean curvature flow for axisymmetric surfaces of genus zero. A careful treatment of the degeneracy at the axis of rotation for the onedimensional partial differential equation for a parameterization of the generating curve allows us to prove error bounds with respect to discrete L2 - and H1 -norms for a fully discrete approximation. The theoretical results are confirmed with the help of numerical convergence experiments. We also present numerical simulations for some genus-0 surfaces, including for a nonembedded self-shrinker for mean curvature flow