Numerical schemes for a three component Cahn-Hilliard model
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 4, p. 697-738

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.

DOI : https://doi.org/10.1051/m2an/2010072
Classification:  35K55,  65M60,  65M12,  76T30
Keywords: finite element, Cahn-Hilliard model, numerical scheme, energy estimate
@article{M2AN_2011__45_4_697_0,
     author = {Boyer, Franck and Minjeaud, Sebastian},
     title = {Numerical schemes for a three component Cahn-Hilliard model},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {45},
     number = {4},
     year = {2011},
     pages = {697-738},
     doi = {10.1051/m2an/2010072},
     zbl = {1267.76127},
     mrnumber = {2804656},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2011__45_4_697_0}
}
Boyer, Franck; Minjeaud, Sebastian. Numerical schemes for a three component Cahn-Hilliard model. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 4, pp. 697-738. doi : 10.1051/m2an/2010072. http://www.numdam.org/item/M2AN_2011__45_4_697_0/

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