An algorithm for Mean Curvature Motion | Zendy

Antonin Chambolle | Zendy

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An algorithm for Mean Curvature Motion

Author(s) -

Antonin Chambolle

Publication year - 2004

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/97

Subject(s) - hypersurface , mean curvature , curvature , motion (physics) , algorithm , anisotropy , mean curvature flow , mathematics , zero (linguistics) , viscosity , mathematical analysis , computer science , geometry , physics , artificial intelligence , optics , linguistics , philosophy , quantum mechanics

We propose in this paper a new algorithm for computing the evolution by mean curvature of a hypersurface. Our algorithm is a variant of the variational approach of Almgren, Taylor and Wang~\cite{ATW}. We show that it approximates, as the time--step goes to zero, the generalized motion(in the sense of barriers or viscosity solutions). The results still hold for the Anisotropic Mean Curvature Motion, as long as the anisotropy is smooth.

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