Numerical surgery for mean curvature flow of surfaces

A numerical algorithm for mean curvature flow of surfaces with surgery is proposed. The method uses a convergent 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.