Rothe’s method for an isothermal phase-field model of a binary alloy with convection

Abstract

A mathematical analysis of a phase-field model for solidification non-isothermal of a binary alloy with convection is presented. Convergence of the solutions of discretized scheme is proved and existence result for original problem are derived.

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

“…With reference to such a complete discretization of Cahn-Hilliard and viscous Cahn-Hilliard systems, we quote papers [1,2,3,4,5,6,7,8,22,21,23]. Some recent efforts can be found in the literature with the aim of analyzing other classes of phase transition problems, either to show existence via time discretization [9,14,15,19,20,27,30,35,36] or to prove numerical results such as special convergence properties, stability or error estimates [11,12,13,18,25,28,31,33,34] (cf. also [26] for a recent review on phase-field models).…”