Finite Element Approximation of the Cahn-Hilliard-Cook equation

Abstract

We study the nonlinear stochastic Cahn-Hilliard equation per- turbed 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.

References in corpus (1)

• Finite element approximation of the linearized Cahn-Hilliard-Cook equation

Cited by in corpus (21)

• On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with non-globally monotone coefficients
• Galerkin Finite Element Approximations for Stochastic Space-Time Fractional Wave Equations
• On the discretisation in time of the stochastic Allen-Cahn equation
• On the backward Euler approximation of the stochastic Allen-Cahn equation
• Optimal error estimates of Galerkin finite element methods for stochastic Allen-Cahn equation with additive noise
• Approximating Stochastic Evolution Equations with Additive White and Rough Noises
• Strong convergence of a fully discrete finite element approximation of the stochastic Cahn-Hilliard equation
• Optimal Strong Rates of Convergence for a Space-Time Discretization of the Stochastic Allen-Cahn Equation with multiplicative noise
• Finite element approximation of the linearized Cahn-Hilliard-Cook equation
• Density convergence of a fully discrete finite difference method for stochastic Cahn--Hilliard equation
• Convergence analysis of a finite difference method for stochastic Cahn--Hilliard equation
• Numerical analysis of a full discretization for stochastic Cahn--Hilliard equation driven by additive noise
• Strong convergence rates of an explicit scheme for stochastic Cahn--Hilliard equation with additive noise
• Weak convergence of the backward Euler method for stochastic Cahn--Hilliard equation with additive noise
• Stochastic Partial Differential Equations on Evolving Surfaces and Evolving Riemannian Manifolds
• Absolute continuity and numerical approximation of stochastic Cahn--Hilliard equation with unbounded noise diffusion
• Asymptotics of large deviations of finite difference method for stochastic Cahn--Hilliard equation
• Analysis of the Morley element for the Cahn-Hilliard equation and the Hele-Shaw flow
• Pathwise existence of solutions to the Implicit Euler method for the stochastic Cahn-Hilliard Equation
• Fully Discrete Mixed Finite Element Methods for the Stochastic Cahn-Hilliard Equation with Gradient-type Multiplicative Noise
• Strong convergence rates of a fully discrete scheme for nonlinear stochastic partial differential equations with non-globally Lipschitz coefficients driven by multiplicative noise