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

Klaus Deckelnick | Zendy

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

Author(s) -

Klaus Deckelnick

Publication year - 2000

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/15

Subject(s) - discretization , mean curvature flow , mathematics , curvature , monotone polygon , regularization (linguistics) , viscosity solution , viscosity , mathematical analysis , mean curvature , flow (mathematics) , space (punctuation) , finite difference , geometry , physics , linguistics , philosophy , quantum mechanics , artificial intelligence , computer science

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 ∞ -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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