Analysis of a time discretization scheme for a nonstandard viscous Cahn--Hilliard system
- Colli, Pierluigi
- Gilardi, Gianni
- Krejčí, Pavel
- Podio-Guidugli, Paolo
- Sprekels, Jürgen
2010 Mathematics Subject Classification
- 35A40 35K55 35Q70 65M12 65M15
- Cahn--Hilliard equation, phase field model, time discretization, convergence, error estimates
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.
- ESAIM Math. Model. Numer. Anal., 48 (2014) pp. 1061--1087.