Geodesic
Convergence of a large time-step scheme for mean curvature motion
Elisabetta Carlini1 ; Maurizio Falcone1 ; R. Ferretti2
1Università di Roma La Sapienza, Italy
2Università di Roma Tre, Italy
Interfaces and free boundaries, Tome 12 (2010) no. 4, pp. 409-441

Voir la notice de l'article provenant de la source EMS Press

DOI

We analyse the properties of a semi-Lagrangian scheme for the approximation of the Mean Curvature Motion (MCM). This approximation is obtained by coupling a stochastic method for the approximation of characteristics (to be understood in a generalized sense) with a local interpolation. The main features of the scheme are that it can handle degeneracies, it is explicit and it allows for large time steps. We also propose a modified version of this scheme, for which monotonicity and consistency can be proved. Then convergence to the viscosity solution of the MCM equation follows by an extension of the Barles–Souganidis theorem. The scheme is also compared with similar existing schemes proposed by Crandall and Lions and, more recently, by Kohn and Serfaty. Finally, several numerical test problems in 2D and 3D are presented.
DOI : 10.4171/ifb/240
Classification : 65-XX, 49-XX, 00-XX
Mots-clés : Mean curvature motion; level-set approach; semi-Lagrangian schemes; consistency; generalized monotonicity; convergence

Elisabetta Carlini  1   ; Maurizio Falcone  1   ; R. Ferretti  2

1 Università di Roma La Sapienza, Italy
2 Università di Roma Tre, Italy 
Elisabetta Carlini; Maurizio Falcone; R. Ferretti. Convergence of a large time-step scheme for mean curvature motion. Interfaces and free boundaries, Tome 12 (2010) no. 4, pp. 409-441. doi: 10.4171/ifb/240
@article{10_4171_ifb_240,
     author = {Elisabetta Carlini and Maurizio Falcone and R. Ferretti},
     title = {Convergence of a large time-step scheme for mean curvature motion},
     journal = {Interfaces and free boundaries},
     pages = {409--441},
     year = {2010},
     volume = {12},
     number = {4},
     doi = {10.4171/ifb/240},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/240/}
}
TY  - JOUR
AU  - Elisabetta Carlini
AU  - Maurizio Falcone
AU  - R. Ferretti
TI  - Convergence of a large time-step scheme for mean curvature motion
JO  - Interfaces and free boundaries
PY  - 2010
SP  - 409
EP  - 441
VL  - 12
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ifb/240/
DO  - 10.4171/ifb/240
ID  - 10_4171_ifb_240
ER  - 
%0 Journal Article
%A Elisabetta Carlini
%A Maurizio Falcone
%A R. Ferretti
%T Convergence of a large time-step scheme for mean curvature motion
%J Interfaces and free boundaries
%D 2010
%P 409-441
%V 12
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/240/
%R 10.4171/ifb/240
%F 10_4171_ifb_240

Cité par Sources :