A finite element error analysis for axisymmetric mean curvature flow

We consider the numerical approximation of axisymmetric mean curvature flow with the help of linear finite elements. In the case of a closed genus-1 surface, we derive optimal error bounds with respect to the $L^2$– and $H^1$–norms for a fully discrete approximation. We perform convergence experiments to confirm the theoretical results, and also present numerical simulations for some genus-0 and genus-1 surfaces, including for the Angenent torus.