Computational anisotropic Willmore flow

Abstract

We study a geometrically consistent formulation of anisotropic Willmore flow for parametric hypersurfaces in ${\mathbb{R}}^n$. After giving a mixed formulation that is suitable for discretization by piecewise linear finite elements, we provide a stable semi-discrete scheme. An experimentally stable fully discrete semi-implicit scheme is then discussed and several tests for the evolution of curves and surfaces are presented.