English

A modified phase field approximation for mean curvature flow with conservation of the volume

Numerical Analysis 2009-04-02 v1 Analysis of PDEs

Abstract

This paper is concerned with the motion of a time dependent hypersurface that evolves by mean curvature flow with a a volume constraint. Phase field approximation of this motion leads to the well known nonlocal Allen--Cahn equation. Here we propose a modified version of this equation, and we show that it has better volume preserving properties than the classical one, even in the presence of an additional forcing term.

Keywords

Cite

@article{arxiv.0904.0098,
  title  = {A modified phase field approximation for mean curvature flow with conservation of the volume},
  author = {Elie Bretin and Morgan Brassel},
  journal= {arXiv preprint arXiv:0904.0098},
  year   = {2009}
}

Comments

34 pages, 19 figures