Study of a finite volume scheme for the regularised mean curvature flow level set equation

Robert Eymard (1) , Angela Handlovicova (2) , Karol Mikula (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 STUBA - Department of Mathematics

We propose a new finite volume numerical scheme for the approximation of regularised mean curvature flow level set equations, which ensures the maximum principle, and which is shown to converge to the solution of the problem. The convergence proof uses the monotonicity of the operator, in order to get the strong convergence of the approximation of the gradient. The regularisation of the original level set problem is practically meaningful and not restrictive, especially when dealing with image processing applications. Numerical examples provide indications about the accuracy of the method.

Keywords: Regularised mean curvature motion equation; convergence of finite volume method; Leray-Lions operators

Domains: Numerical Analysis [math.NA]

Robert Eymard, Angela Handlovicova, Karol Mikula. Study of a finite volume scheme for the regularised mean curvature flow level set equation. IMA Journal of Numerical Analysis, 2011, http://imajna.oxfordjournals.org/content/31/3/813. ⟨10.1093/imanum/drq025⟩. ⟨hal-00407573v2⟩