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

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" finite element method with numerical integration which includes a standard finite difference approximation. The time discretization is the backward Euler scheme. The smallness assumption on the time step does not depend on the mesh step.
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https://hal-normandie-univ.archives-ouvertes.fr/hal-01777572
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Submitted on : Tuesday, April 24, 2018 - 9:07:32 PM
Last modification on : Tuesday, August 13, 2019 - 11:10:04 AM

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Maurizio Grasselli, N. Lecoq, Morgan Pierre. A long-time stable fully discrete approximation of the Cahn-Hilliard equation with inertial term. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS SUPPLEMENT, American Institude of Mathematical Sciences, 2011, pp.543-552. ⟨10.3934/proc.2011.2011.543⟩. ⟨hal-01777572⟩

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