A semi-Lagrangian scheme for mean curvature motion with nonlinear Neumann conditions | Zendy

Yves Achdou | Zendy; Maurizio Falcone | Zendy

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A semi-Lagrangian scheme for mean curvature motion with nonlinear Neumann conditions

Author(s) -

Yves Achdou,

Maurizio Falcone

Publication year - 2013

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/288

Subject(s) - mathematics , boundary (topology) , mean curvature , neumann boundary condition , nonlinear system , curvature , domain (mathematical analysis) , mathematical analysis , bounded function , mean curvature flow , monotonic function , polygon mesh , scheme (mathematics) , dimension (graph theory) , motion (physics) , consistency (knowledge bases) , geometry , classical mechanics , pure mathematics , physics , quantum mechanics

A numerical method for mean curvature motion in bounded domains with nonlinear Neumann boundary conditions is proposed and analyzed. It consists of a semi-Lagrangian scheme in the main part of the domain as proposed by Carlini, Falcone and Ferretti, combined with a finite difference scheme in small layers near the boundary to cope with the boundary condition. The consistency of the new scheme is proved for nonstructured triangular meshes in dimension two. The monotonicity of a regularized version of the scheme with some additional vanishing artificial viscosity is studied. Details on the implementation are given. Numerical tests are presented.

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