2011, 2011(Special): 543-552. doi: 10.3934/proc.2011.2011.543

A long-time stable fully discrete approximation of the Cahn-Hilliard equation with inertial term

1. 

Dipartimento di Matematica, Politecnico di Milano, 20133 Milano

2. 

Groupe de Physique de Matériaux UMR CNRS6634, Université de Rouen, 1, Avenue de l'Université, 76801 Saint-Etienne du Rouvray, France

3. 

Laboratoire de Mathématiques et Applications UMR CNRS 6086, Université de Poitiers, Téléport 2 - BP 30179, Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil

Received  June 2010 Revised  April 2011 Published  October 2011

We prove the Lyapunov stability of a time and space discretization of the Cahn-Hilliard equation with inertial term. The space discretization is a mixed (or "splitting") nite element method with numerical integration which includes a standard nite di erence approximation. The time discretization is the backward Euler scheme. The smallness assumption on the time step does not depend on the mesh step.
Citation: Maurizio Grasselli, Nicolas Lecoq, Morgan Pierre. A long-time stable fully discrete approximation of the Cahn-Hilliard equation with inertial term. Conference Publications, 2011, 2011 (Special) : 543-552. doi: 10.3934/proc.2011.2011.543
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