JournalsifbVol. 2, No. 2pp. 117–142

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

  • Klaus Deckelnick

    Otto-von-Guericke-Universität Magdeburg, Germany
Error bounds for a difference scheme approximating viscosity solutions of mean curvature flow cover
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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.

Cite this article

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

DOI 10.4171/IFB/15