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 one dimensional partial differential equation for a parameterization of the generating curve allows us to prove error bounds with respect to discrete $L^2$- and $H^1$-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 non-embedded self-shrinker for mean curvature flow.

翻译：我们考虑对genus 零的轴向表面平均曲率流的有限差差近差。 仔细处理生成曲线参数化的单维部分偏差方程式旋转轴的退化性, 使我们能够证明离散值$L $2$- 和$H $1$- 诺尔姆的差错界限。 理论结果在数字趋同实验的帮助下得到确认。 我们还对某些genus- 0 的表面进行数字模拟, 包括对中值曲线流的非嵌入式自我磨损器进行模拟 。