Error estimates for time discretizations of Cahn-Hilliard and Allen-Cahn phase-field models for two-phase incompressible flows

摘要

We carry out rigorous error analysis for some energy stable time discretization schemes developed in Shen and Yang (SIAM J Sci Comput 32(3):1159-1179, 2010) for a Cahn-Hilliard phase-field model and in Shen and Yang (Chin Ann Math Ser B 31(5):743-758, 2010) for an Allen-Cahn phase-field model.