Strong Convergence of a Fully Discrete Finite Element Approximation of the Stochastic Cahn--Hilliard Equation

Finite Element Approximation of the Cahn-Hilliard-Cook Equation

We study the nonlinear stochastic Cahn-Hilliard equation driven by additive colored noise. We show almost sure existence and regularity of solutions. We introduce spatial approximation by a standard finite element method and prove error estimates of optimal order on sets of probability arbitrarily close to 1. We also prove strong convergence without known rate.

Finite Element Approximation of the Linearized Cahn-hilliard-cook Equation

The linearized Cahn-Hilliard-Cook equation is discretized in the spatial variables by a standard finite element method. Strong convergence estimates are proved under suitable assumptions on the covariance operator of the Wiener process, which is driving the equation. The backward Euler time stepping is also studied. The analysis is set in a framework based on analytic semigroups. The main part ...

Erratum: Finite Element Approximation of the Cahn-Hilliard-Cook Equation

We prove an additional result on the linearized Cahn-HilliardCook equation to fill in a gap in the main argument in our paper which was published in SIAM J. Numer. Anal. 49 (2011), 2407–2429. The result is a pathwise error estimate, which is proved by an application of the factorization argument for stochastic convolutions.

Convergence analysis of a fully discrete finite difference scheme for the Cahn-Hilliard-Hele-Shaw equation

We present an error analysis for an unconditionally energy stable, fully discrete finite difference scheme for the Cahn-Hilliard-Hele-Shaw equation, a modified Cahn-Hilliard equation coupled with the Darcy flow law. The scheme, proposed in [47], is based on the idea of convex splitting. In this paper, we rigorously prove first order convergence in time and second order convergence in space. Ins...

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