Anisotropic mean curvature flow for two-dimensional surfaces in higher codimension: a numerical scheme

Abstract

We consider evolution of two dimensional parametric surfaces by ani\-sotropic mean curvature flow in ${\mathbb{R}}^n$, for arbitrary $n\ge 3$. After deriving a classical and a weak formulation of the flow, a fully discrete stable finite element scheme is proposed, and numerical tests and simulations are presented.