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Numerical schemes for a threecomponentCahn-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

Abstract

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In this article, we investigate numerical schemes for solvinga three component Cahn-Hilliard model. The space discretization isperformed by usinga 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 energyand thus the stability of the method.We study three different schemes and proveexistence and convergence theorems. Theoretical results areillustrated by various numerical examples showing that the new semi-implicitdiscretization that we propose seems to be a good compromise between robustnessand accuracy.

Keywords

Finite elementCahn-Hilliard modelnumerical schemeenergy estimate

Information

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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