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.
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Klaus Deckelnick, Error bounds for a difference scheme approximating viscosity solutions of mean curvature flow. Interfaces Free Bound. 2 (2000), no. 2, pp. 117–142DOI 10.4171/IFB/15