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Finite Volume approximation of a two-phase two fluxes degenerate Cahn-Hilliard model

Abstract : We study a time implicit Finite Volume scheme for degenerate Cahn-Hilliard model proposed in [W. E and P. Palffy-Muhoray. Phys. Rev. E, 55:R3844R3846, 1997] and studied mathematically by the authors in [C. Cancès, D. Matthes, and F. Nabet. Arch. Ration. Mech. Anal., 233(2):837-866, 2019]. The scheme is shown to preserve the key properties of the continuous model, namely mass conservation, positivity of the concentrations, the decay of the energy and the control of the entropy dissipation rate. This allows to establish the existence of a solution to the nonlinear algebraic system corresponding to the scheme. Further, we show thanks to compactness arguments that the approximate solution converges towards a weak solution of the continuous problems as the discretization parameters tend to 0. Numerical results illustrate the behavior of the numerical model.
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Contributor : Clément Cancès Connect in order to contact the contributor
Submitted on : Monday, January 18, 2021 - 9:38:00 AM
Last modification on : Thursday, May 6, 2021 - 9:28:07 AM

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Clément Cancès, Flore Nabet. Finite Volume approximation of a two-phase two fluxes degenerate Cahn-Hilliard model. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2021, 55 (3), pp.969--1003. ⟨10.1051/m2an/2021002⟩. ⟨hal-02561981v3⟩

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