Adaptive finite element methods for Cahn-Hilliard equations

We develop a method for adaptive mesh refinement for steady state problems that arise in the numerical solution of Cahn-Hilliard equations with an obstacle free energy. The problem is discretized in time by the backward-Euler method and in space by linear finite elements. The adaptive mesh refinement is performed using residual based a posteriori estimates; the time step is adapted using a heuristic criterion. We describe the space-time adaptive algorithm and present numerical experiments in two and three space dimensions that demonstrate the usefulness of our approach. © 2007 Elsevier B.V. All rights reserved.