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Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2012

Phase field method for mean curvature flow with boundary constraints

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Abstract

This paper is concerned with the numerical approximation of mean curvature flow $t \to \Omega(t)$ satisfying an additional inclusion-exclusion constraint $\Omega_1 \subset \Omega(t) \subset \Omega_2$. 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 $\Gamma$-convergence result and then show some numerical comparisons of these two different models.
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Dates and versions

hal-00587755 , version 1 (23-04-2011)

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Elie Bretin, Valérie Perrier. Phase field method for mean curvature flow with boundary constraints. ESAIM: Mathematical Modelling and Numerical Analysis, 2012, 46 (6), pp.1509-1526. ⟨10.1051/m2an/2012014⟩. ⟨hal-00587755⟩
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