Numerical schemes for a three component Cahn-Hilliard model

Franck Boyer; Sebastian Minjeaud

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

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

Abstract

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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.

How to cite

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Boyer, Franck, and Minjeaud, Sebastian. "Numerical schemes for a three component Cahn-Hilliard model." ESAIM: Mathematical Modelling and Numerical Analysis 45.4 (2011): 697-738. <http://eudml.org/doc/197597>.

@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},
keywords = {Finite element; Cahn-Hilliard model; numerical scheme; energy estimate; finite element; energy estimate},
language = {eng},
month = {1},
number = {4},
pages = {697-738},
publisher = {EDP Sciences},
title = {Numerical schemes for a three component Cahn-Hilliard model},
url = {http://eudml.org/doc/197597},
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
DA - 2011/1//
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; finite element; energy estimate
UR - http://eudml.org/doc/197597
ER -

References

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