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Numerical schemes for a threecomponent Cahn-Hilliard model

Published online by Cambridge University Press:  10 December 2010

Franck Boyer
Université Paul Cézanne, FST Saint-Jérôme, Case cour A, LATP, Avenue Escadrille Normandie-Niemen, 13397 Marseille Cedex 20, France.
Sebastian Minjeaud
Institut de Radioprotection et de Sûreté Nucléaire, Bât. 702, BP3, 13115 Saint Paul lez Durance, France.
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In this article, we investigate numerical schemes for solving a three component Cahn-Hilliard model. The space discretization is performed by using a Galerkin formulation and the finite element method. Concerning the time discretization, the main difficulty is to write a scheme ensuring, at the discrete level, the decrease of the free energy and thus the stability of the method. We study three different schemes and prove existence and convergence theorems. Theoretical results are illustrated by various numerical examples showing that the new semi-implicit discretization that we propose seems to be a good compromise between robustness and accuracy.

Research Article
© EDP Sciences, SMAI, 2010

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