A numerical algorithm for mean curvature flow of closed mean convex surfaces with surgery is proposed. The method uses a finite element based mean curvature flow algorithm based on a coupled partial differential equation system which directly provides an approximation for mean curvature and outward unit normal. The proposed numerical surgery process closely follows the analytical surgery of Huisken \& Sinestrari, and Brendle \& Huisken. The numerical surgery approach is described in detail, along with extensions to other geometric flows and methods. Numerical experiments report on the performance of the numerical surgery process.

翻译：提出了一种面向闭平均凸曲面进行手术操作的平均曲率流数值算法。该方法基于耦合偏微分方程组构建有限元平均曲率流算法，可直接获得平均曲率与单位外法向量的近似值。所提出的数值手术过程紧密遵循Huisken & Sinestrari以及Brendle & Huisken提出的解析手术框架。本文详细阐述了数值手术方法，并探讨了其在其他几何流处理及方法中的扩展应用。数值实验报告了该数值手术过程的性能表现。