# Numerical schemes for a three component Cahn-Hilliard model

Franck Boyer; Sebastian Minjeaud

- Volume: 45, Issue: 4, page 697-738
- ISSN: 0764-583X

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topBoyer, Franck, and Minjeaud, Sebastian. "Numerical schemes for a three component Cahn-Hilliard model." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 45.4 (2011): 697-738. <http://eudml.org/doc/273344>.

@article{Boyer2011,

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.},

author = {Boyer, Franck, Minjeaud, Sebastian},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {finite element; Cahn-Hilliard model; numerical scheme; energy estimate},

language = {eng},

number = {4},

pages = {697-738},

publisher = {EDP-Sciences},

title = {Numerical schemes for a three component Cahn-Hilliard model},

url = {http://eudml.org/doc/273344},

volume = {45},

year = {2011},

}

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 - Modélisation Mathématique et Analyse Numérique

PY - 2011

PB - EDP-Sciences

VL - 45

IS - 4

SP - 697

EP - 738

AB - 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.

LA - eng

KW - finite element; Cahn-Hilliard model; numerical scheme; energy estimate

UR - http://eudml.org/doc/273344

ER -

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