A nonconforming finite element method for the Cahn-Hilliard equation

Authors:
Shuo Zhang;Ming Wang
Affiliations:
LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, PR China;LMAM School of Mathematical Sciences, Peking University, Beijing 100871, PR China
Venue:
Journal of Computational Physics
Year:
2010

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Abstract

This paper reports a fully discretized scheme for the Cahn-Hilliard equation. The method uses a convexity-splitting scheme to discretize in the temporal variable and a nonconforming finite element method to discretize in the spatial variable. And, the scheme can preserve the mass conservation and energy dissipation properties of the original problem. Some typical phase transition phenomena are also observed through the numerical examples.