A multigrid finite element solver for the Cahn-Hilliard equation

A multigrid finite element solver for the Cahn-Hilliard equation is presented that has mesh-independent convergence rates for any time-step size, including in the important limit epsilon -> 0 which is examined via numerical examples. Numerics are performed for a number of test problems which show that the features of the Cahn-Hilliard equation (minimising interface measure, Lyapunov energy functional etc.) are preserved. We also explore the use of this solver in conjunction with adaptive time-stepping and adaptive mesh strategies. (c) 2005 Elsevier Inc. All rights reserved.