Geodesic
Error bounds for a difference scheme approximating viscosity solutions of mean curvature flow
Klaus Deckelnick1
1Otto-von-Guericke-Universität Magdeburg, Germany
Interfaces and free boundaries, Tome 2 (2000) no. 2, pp. 117-142

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DOI

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.
DOI : 10.4171/ifb/15
Classification : 46-XX, 60-XX
Mots-clés : finite difference schemes; mean curvature flow

Klaus Deckelnick  1

1 Otto-von-Guericke-Universität Magdeburg, Germany 
Klaus Deckelnick. Error bounds for a difference scheme approximating viscosity solutions of mean curvature flow. Interfaces and free boundaries, Tome 2 (2000) no. 2, pp. 117-142. doi: 10.4171/ifb/15
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     title = {Error bounds for a difference scheme approximating viscosity solutions of mean curvature flow},
     journal = {Interfaces and free boundaries},
     pages = {117--142},
     year = {2000},
     volume = {2},
     number = {2},
     doi = {10.4171/ifb/15},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/15/}
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