Kovacs Mihaly (Pazmany Peter Katolikus Egyetem): Numerical approximation of the Cahn-Hilliard-Cook equation

We consider the stochastic Cahn-Hilliard equation, also known as the Cahn-Hilliard-Cook

equation, which describes phase separation in a binary alloy that undergoes rapid cooling.

The noise, called the Cook term, is additive, Gaussian and models thermal fluctuations during

the cooling process. Mathematically, the Cahn-Hilliard-Cook equation is a semilinear, parabolic,

stochastic partial differential equation with a nonlinear drift term which fails to be globally Lipschitz

continuous, or even one-sided Lipschitz continuous or globally monotone. The equation is discretized

by a finite element method complemented by Backward Euler time stepping. In the talk we outline

how to prove strong convergence of the approximation as the discretization parameters vanish.