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

We study a time implicit Finite Volume scheme for degenerate Cahn–Hilliard model proposed in [W. E and P. Palffy-Muhoray, Phys. Rev. 55 (1997) R3844–R3846] studied mathematically by the authors [C. Cancès, D. Matthes F. Nabet, Arch. Ration. Mech. Anal. 233 (2019) 837–866]. The is shown to preserve key properties of continuous model, namely mass conservation, positivity concentrations, decay energy control entropy dissipation rate. This allows establish existence solution nonlinear algebraic system corresponding scheme. Further, we show thanks compactness arguments that approximate converges towards weak problems as discretization parameters tend 0. Numerical results illustrate behavior numerical model.