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

Pages: 543 - 552, Issue Special, September 2011

 Abstract        Full Text (311.4K)              

Maurizio Grasselli - Dipartimento di Matematica, Politecnico di Milano, 20133 Milano, Italy (email)
Nicolas Lecoq - Groupe de Physique de Matériaux UMR CNRS6634, Université de Rouen, 1, Avenue de l'Université, 76801 Saint-Etienne du Rouvray, France (email)
Morgan Pierre - Laboratoire de Mathématiques et Applications UMR CNRS 6086, Université de Poitiers, Téléport 2 - BP 30179, Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil, France (email)

Abstract: 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.

Keywords:  Second-order gradient-like ow, Cahn-Hilliard equation, mixed nite elements, discrete negative norms, numerical integration, Lojasiewicz inequality
Mathematics Subject Classification:  Primary: 65M12, 82C26; Secondary: 65M60, 65P40

Received: June 2010;      Revised: April 2011;      Published: October 2011.