Finite Element Approximation of the Cahn-Hilliard Equation with Degenerate Mobility

Finite element approximation of the Cahn-Hilliard equation with concentration dependent mobility

We consider the Cahn-Hilliard equation with a logarithmic free energy and non-degenerate concentration dependent mobility. In particular we prove that there exists a unique solution for sufficiently smooth initial data. Further, we prove an error bound for a fully practical piecewise linear finite element approximation in one and two space dimensions. Finally some numerical experiments are pres...

On the Cahn{hilliard Equation with Non{constant Mobility and Its Asymptotic Limit

We present an existence result for the Cahn{Hilliard equation with a concentration dependent mobility which allows the mobility to degenerate. Formal asymptotic results relate the Cahn{Hilliard equation with a degenerate mobility to motion by surface diiusion V = ? S. We state a local existence result for this geometric motion and show that circles are asymptotically stable.

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.

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

On the Cahn{hilliard Equation with Degenerate Mobility

An existence result for the Cahn{Hilliard equation with a concentration dependent diiusional mobility is presented. In particular the mobility is allowed to vanish when the scaled concentration takes the values 1 and it is shown that the solution is bounded by 1 in magnitude. Finally applications of our method to other degenerate fourth order parabolic equations are discussed.