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Phase field method for mean curvature flow with boundary constraints

Elie BretinValerie Perrier — 2012

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is concerned with the numerical approximation of mean curvature flow  → () satisfying an additional inclusion-exclusion constraint  ⊂ () ⊂  . 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...

Phase field method for mean curvature flow with boundary constraints

Elie BretinValerie Perrier — 2012

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is concerned with the numerical approximation of mean curvature flow  → () satisfying an additional inclusion-exclusion constraint  ⊂ () ⊂  . 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...

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