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.
Mots clés : 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 }, pages = {697--738}, publisher = {EDP-Sciences}, volume = {45}, number = {4}, year = {2011}, doi = {10.1051/m2an/2010072}, mrnumber = {2804656}, zbl = {1267.76127}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2010072/} }
TY - JOUR AU - Boyer, Franck AU - Minjeaud, Sebastian TI - Numerical schemes for a three component Cahn-Hilliard model JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2011 SP - 697 EP - 738 VL - 45 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2010072/ DO - 10.1051/m2an/2010072 LA - en ID - M2AN_2011__45_4_697_0 ER -
%0 Journal Article %A Boyer, Franck %A Minjeaud, Sebastian %T Numerical schemes for a three component Cahn-Hilliard model %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2011 %P 697-738 %V 45 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2010072/ %R 10.1051/m2an/2010072 %G en %F 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 , Tome 45 (2011) no. 4, pp. 697-738. doi : 10.1051/m2an/2010072. http://www.numdam.org/articles/10.1051/m2an/2010072/
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