A multigrid finite element solver for the Cahn-Hilliard equation

Authors:
David Kay;Richard Welford
Affiliations:
Department of Mathematics, Mantell Building, University of Sussex, Falmer, Brighton, BN1 9RF, UK;Department of Mathematics, Mantell Building, University of Sussex, Falmer, Brighton, BN1 9RF, UK
Venue:
Journal of Computational Physics
Year:
2006

Citing 3
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Abstract

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 @e-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.