Elementary discrete diffusion/redistancing schemes for the mean curvature flow

TL;DR

This paper introduces a simple, explicit numerical scheme for simulating mean curvature flow, with proven convergence under standard conditions and potential extensions to more complex schemes.

Contribution

It presents an elementary, fully discrete scheme for mean curvature flow with a convergence proof and discusses possible extensions to other convolution-based methods.

Findings

The scheme converges under the CFL condition h ~ ε^2.

The scheme is based on an elementary diffusion and redistancing operation.

Extensions to more general schemes are discussed.

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.