Phase field method for mean curvature flow with boundary constraints
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...