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A multigrid method for the Cahn-Hilliard equation with obstacle potential. (English) Zbl 1168.65386
Summary: We present a multigrid finite element method for the deep quench obstacle Cahn-Hilliard equation. The non-smooth nature of this highly nonlinear fourth order partial differential equation make this problem particularly challenging. The method exhibits mesh-independent convergence properties in practice for arbitrary time step sizes. In addition, numerical evidence shows that this behaviour extends to small values of the interfacial parameter $$\gamma$$. Several numerical examples are given, including comparisons with existing alternative solution methods for the Cahn-Hilliard equation.

##### MSC:
 65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 35Q53 KdV equations (Korteweg-de Vries equations) 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
ALBERTA
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