Analysis of a time discretization scheme for a nonstandard viscous Cahn-Hilliard system

0430395 - MÚ 2015 RIV FR eng J - Journal Article
Colli, P. - Gilardi, G. - Krejčí, Pavel - Podio-Guidugli, P. - Sprekels, J.
Analysis of a time discretization scheme for a nonstandard viscous Cahn-Hilliard system.
E S A I M: Mathematical Modelling and Numerical Analysis. Roč. 48, č. 4 (2014), s. 1061-1087. ISSN 0764-583X. E-ISSN 1290-3841
R&D Projects: GA ČR GAP201/10/2315
Institutional support: RVO:67985840
Keywords : Cahn-Hillard equation * convergence * error estimates
Subject RIV: BA - General Mathematics
Impact factor: 1.642, year: 2014
http://www.esaim-m2an.org/articles/m2an/abs/2014/04/m2an140005/m2an140005.html

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.
Permanent Link: http://hdl.handle.net/11104/0235349