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Numerical schemes for a threecomponent Cahn-Hilliard model

Published online by Cambridge University Press:  10 December 2010

Franck Boyer  and
Sebastian Minjeaud
Franck Boyer
Affiliation:
Université Paul Cézanne, FST Saint-Jérôme, Case cour A, LATP, Avenue Escadrille Normandie-Niemen, 13397 Marseille Cedex 20, France. fboyer@latp.univ-mrs.fr
Sebastian Minjeaud
Affiliation:
Institut de Radioprotection et de Sûreté Nucléaire, Bât. 702, BP3, 13115 Saint Paul lez Durance, France. sebastian.minjeaud@irsn.fr
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Abstract

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.

Keywords

Finite elementCahn-Hilliard modelnumerical schemeenergy estimate
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 4 , July 2011 , pp. 697 - 738
Copyright
© EDP Sciences, SMAI, 2010

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