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 ϵ → 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.