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Author: Colli, Pierluigi × Author: Krejcí, Pavel × Author: Podio-Guidugli, Paola ×

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    Analysis of a time discretization scheme for a nonstandard viscous Cahn-Hilliard system
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Colli, Pierluigi; Gilardi, Gianni; Krejcí, Pavel; Podio-Guidugli, Paola; Sprekels, Jürgen
    In this paper we propose a time discretization of a system of two parabolic equations describing diffusion-driven atom rearrangement in crystalline matter. The equations express the balances of microforces and microenergy; the two phase fields are the order parameter and the chemical potential. The initial and boundary-value problem for the evolutionary system is known to be well posed. Convergence of the discrete scheme to the solution of the continuous problem is proved by a careful development of uniform estimates, by weak compactness and a suitable treatment of nonlinearities. Moreover, for the difference of discrete and continuous solutions we prove an error estimate of order one with respect to the time step.