Error bounds for a difference scheme approximating viscosity solutions of mean curvature flow

Abstract

We analyse a finite difference scheme for the approximation of level set solutions to mean curvature flow. The scheme which was proposed by Crandall & Lions (Numer. Math. 75, (1996) 17-41) is a monotone and consistent discretization of a regularized version of the underlying problem. We derive an L[infin]-error bound between the numerical solution and the viscosity solution to the level set equation provided that the space and time step sizes are appropriately related to the regularization parameter.