Elementary discrete diffusion/redistancing schemes for the mean curvature flow

Abstract

We consider a fully discrete and explicit scheme for the mean curvature flow of boundaries, based on an elementary diffusion step and a precise redistancing operation. We give an elementary convergence proof for the scheme under the standard CFL condition $h\sim\e^2$, where $h$ is the time discretization step and $\e$ the space step. We discuss extensions to more general convolution/redistancing schemes.