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

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...

Finite Element Approximation of a Degenerate Allen-Cahn/Cahn-Hilliard System

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...

An Error Bound for the Finite Element Approximation of the Cahn-Hilliard Equation with Logarithmic Free Energy

An error bound is proved for a fully practical piecewise linear nite element approximation, using a backward Euler time discretization, of the Cahn-Hilliard equation with a logarithmic free energy.