A multigrid method for the Cahn–Hilliard equation with obstacle potential

Abstract

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 γ . Several numerical examples are given, including comparisons with existing alternative solution methods for the Cahn–Hilliard equation.