TY - GEN A1 - Colli, Pierluigi A1 - Gilardi, Gianni A1 - Krejcí, Pavel A1 - Paolo, Podio-Guidugli A1 - Jürgen, Sprekels T1 - Analysis of a time discretization scheme for a nonstandard viscous Cahn--Hilliard system N2 - 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. KW - Cahn--Hilliard equation KW - phase field model KW - time discretization KW - convergence KW - error estimates Y1 - 2015 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1221 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-12211 ER -