A convolution thresholding scheme for the Willmore flow

Abstract

A convolution thresholding approximation scheme for the Willmore geometric flow is constructed. It is based on an asymptotic expansion of the convolution of an indicator function with a smooth, isotropic kernel. The consistency of the method is justified when the evolving surface is smooth and embedded. Some aspects of the numerical implementation of the scheme are discussed and several numerical results are presented. Numerical experiments show that the method performs well even in the case of a non-smooth initial data.