An approximate factorization/least squares solution method for a mixed finite element approximation of the Cahn-Hilliard equation

We discuss in this article the numerical solution of the Cahn-Hilliard equation modelling the spinodal decomposition of binary alloys. The numerical methodology combines a second-order finite difference time discretization with a mixed finite element space approximation and a least squares formulation based on an approximate factorization of a fourth-order elliptic operator which appears in the numerical model. The least squares problem—which is linear—is solved by a preconditioned conjugate gradient algorithm. The results of numerical experiments illustrate the possibilities of the methods discussed in this article.

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