| Issue |
ESAIM: M2AN
Volume 46, Number 6, November-December 2012
|
|
|---|---|---|
| Page(s) | 1509 - 1526 | |
| DOI | https://doi.org/10.1051/m2an/2012014 | |
| Published online | 13 June 2012 | |
Phase field method for mean curvature flow with boundary constraints
1
CMAP, École Polytechnique, 91128
Palaiseau,
France
bretin@polytechnique.fr
2
Laboratoire Jean Kuntzmann, Université de Grenoble and CNRS, UMR
5224, B.P. 53,
38041
Grenoble Cedex 9,
France
Valerie.Perrier@imag.fr
Received: 14 April 2011
Revised: 9 January 2012
This paper is concerned with the numerical approximation of mean curvature flow t → Ω(t) satisfying an additional inclusion-exclusion constraint Ω1 ⊂ Ω(t) ⊂ Ω2. Classical phase field model to approximate these evolving interfaces consists in solving the Allen-Cahn equation with Dirichlet boundary conditions. In this work, we introduce a new phase field model, which can be viewed as an Allen Cahn equation with a penalized double well potential. We first justify this method by a Γ-convergence result and then show some numerical comparisons of these two different models.
Mathematics Subject Classification: 49Q / 35B / 35K
Key words: Allen Cahn equation / mean curvature flow / boundary constraints / penalization technique / gamma-convergence / Fourier splitting method
© EDP Sciences, SMAI, 2012
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