Geodesic
A semi-Lagrangian scheme for mean curvature motion with nonlinear Neumann conditions
Yves Achdou1 ; Maurizio Falcone2
1Université Paris Diderot, France
2Università di Roma La Sapienza, Italy
Interfaces and free boundaries, Tome 14 (2012) no. 4, pp. 455-485

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DOI

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.
DOI : 10.4171/ifb/288
Classification : 65-XX, 49-XX, 00-XX
Mots-clés : Hamilton Jacobi equations, front propagation, Neumann boundary conditions, convergence, viscosity solutions, triangular meshes

Yves Achdou  1   ; Maurizio Falcone  2

1 Université Paris Diderot, France
2 Università di Roma La Sapienza, Italy 
Yves Achdou; Maurizio Falcone. A semi-Lagrangian scheme for mean curvature motion with nonlinear Neumann conditions. Interfaces and free boundaries, Tome 14 (2012) no. 4, pp. 455-485. doi: 10.4171/ifb/288
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     title = {A {semi-Lagrangian} scheme for mean curvature motion with nonlinear {Neumann} conditions},
     journal = {Interfaces and free boundaries},
     pages = {455--485},
     year = {2012},
     volume = {14},
     number = {4},
     doi = {10.4171/ifb/288},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/288/}
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