A semi-Lagrangian scheme for mean curvature motion with nonlinear Neumann conditions
type: Item
instance of: scholarly article
title: A semi-Lagrangian scheme for mean curvature motion with nonlinear Neumann conditions
zbMATH Open document ID: 1266.65139
DOI: 10.4171/IFB/288
author: M. Falcone
author: Yves Achdou
published in: Interfaces and Free Boundaries
publication date: 2013-04-12T00:00:00Z
review text: 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 \textit{E. Carlini}, \textit{M. Falcone} and \textit{R. Ferretti} [Interfaces Free Bound. 12, No. 4, 409--441 (2010; Zbl 1416.65304)], 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.
reviewed by: Nina Shokina
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 49L25
Mathematics Subject Classification ID: 35F21
Mathematics Subject Classification ID: 65M50
zbMATH DE Number: 6153552
zbMATH Keywords: Hamilton Jacobi equations
zbMATH Keywords: front propagation
zbMATH Keywords: Neumann boundary conditions
zbMATH Keywords: convergence
zbMATH Keywords: viscosity solutions
zbMATH Keywords: triangular meshes
zbMATH Keywords: numerical examples
zbMATH Keywords: mean curvature motion
zbMATH Keywords: semi-Lagrangian scheme
zbMATH Keywords: finite difference scheme
zbMATH Keywords: consistency
zbMATH Keywords: artificial viscosity
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6153552