Parallel Energy-Stable Solver for a Coupled Allen--Cahn and Cahn--Hilliard System

Triple Junction Motion for Allen-Cahn/Cahn-Hilliard Systems

Long time asymptotics are developed here for an Allen-Cahn/Cahn-Hilliard system derived recently by Cahn & Novick-Cohen [11] as a di use interface model for simultaneous orderdisorder and phase separation. Proximity to a deep quench limit is assumed, and spatial scales are chosen to model Krzanowski instabilities in which droplets of a minor disordered phase bounded by interphase boundaries (IP...

Numerical Approximations of Allen-cahn and Cahn-hilliard Equations

Stability analyses and error estimates are carried out for a number of commonly used numerical schemes for the Allen-Cahn and Cahn-Hilliard equations. It is shown that all the schemes we considered are either unconditionally energy stable, or conditionally energy stable with reasonable stability conditions in the semi-discretized versions. Error estimates for selected schemes with a spectral-Ga...

2 Finite Element Approximation of an Allen - Cahn / Cahn - Hilliard

The existence of global attractor for a Cahn-Hilliard/Allen-Cahn‎ ‎equation

In this paper, we consider a Cahn-Hillard/Allen-Cahn equation. By using the semigroup and the classical existence theorem of global attractors, we give the existence of the global attractor in H^k(0

Application of the Local DiscontinuousGalerkinMethod for the Allen-Cahn/Cahn-Hilliard System

In this paper, we consider the application of the local discontinuous Galerkin method for the Allen-Cahn/Cahn-Hilliard system. The method in this paper extends the local discontinuous Galerkin method in [10] to the more general application system which is coupled with the Allen-Cahn and Cahn-Hilliard equations. Similar energy stability result as that in [10] is presented. Numerical results for ...