On the viscous Allen-Cahn and Cahn-Hilliard systems with willmore regularization

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

Error control for the approximation of Allen-Cahn and Cahn-Hilliard equations with a logarithmic potential

A fully computable upper bound for the finite element approximation error of Allen– Cahn and Cahn–Hilliard equations with logarithmic potentials is derived. Numerical experiments show that for the sharp interface limit this bound is robust past topological changes. Modifications of the abstract results to derive quasi-optimal error estimates in different norms for lowest order finite element me...

On Cahn-hilliard Systems with Elasticity