Analysis of a time discretization scheme for a nonstandard viscous Cahn-Hilliard system
arXiv:1304.4503 · doi:10.1051/m2an/2014005
Abstract
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.
Key words: Cahn-Hilliard equation, phase field model, time discretization, convergence, error estimates