# Phase field method for mean curvature flow with boundary constraints

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

- Volume: 46, Issue: 6, page 1509-1526
- ISSN: 0764-583X

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topBretin, Elie, and Perrier, Valerie. "Phase field method for mean curvature flow with boundary constraints." ESAIM: Mathematical Modelling and Numerical Analysis 46.6 (2012): 1509-1526. <http://eudml.org/doc/276375>.

@article{Bretin2012,

abstract = {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.},

author = {Bretin, Elie, Perrier, Valerie},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Allen Cahn equation; mean curvature flow; boundary constraints; penalization technique; gamma-convergence; Fourier splitting method; numerical tests; convergence},

language = {eng},

month = {6},

number = {6},

pages = {1509-1526},

publisher = {EDP Sciences},

title = {Phase field method for mean curvature flow with boundary constraints},

url = {http://eudml.org/doc/276375},

volume = {46},

year = {2012},

}

TY - JOUR

AU - Bretin, Elie

AU - Perrier, Valerie

TI - Phase field method for mean curvature flow with boundary constraints

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2012/6//

PB - EDP Sciences

VL - 46

IS - 6

SP - 1509

EP - 1526

AB - 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.

LA - eng

KW - Allen Cahn equation; mean curvature flow; boundary constraints; penalization technique; gamma-convergence; Fourier splitting method; numerical tests; convergence

UR - http://eudml.org/doc/276375

ER -

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