D. Kay, R. Welford

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 coverage rates for any time-step size, including in the important limit as epsilon goes to zero 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 (minimaising interfase measure, Lyapunov energy function etc.) are preserved. We also explore the use of this solver in conjuction with adaptive mesh strategies.

 Bibliographical note: Submitted to Elsevier Science 11th July 2005.