Finite element approximation of the linearized Cahn-Hilliard-Cook equation
arXiv:2608.12833 · doi:10.1093/imanum/drq042
Abstract
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 effort is spent on proving detailed error bounds for the corresponding deterministic Cahn-Hilliard equation. The results should be interpreted as results on approximation of the stochastic convolution, which is a part of the mild solution of the nonlinear Cahn-Hilliard-Cook equation.
References in corpus (2)
Cited by in corpus (10)
- Finite Element Approximation of the Cahn-Hilliard-Cook equation
- Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise II. Fully discrete schemes
- Strong convergence of a fully discrete finite element approximation of the stochastic Cahn-Hilliard 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
- Weak convergence of the backward Euler method for stochastic Cahn--Hilliard equation with additive noise
- Strong convergence rates of an explicit scheme for stochastic Cahn--Hilliard equation with additive noise
- Asymptotics of large deviations of finite difference method for stochastic Cahn--Hilliard equation
- Fully Discrete Mixed Finite Element Methods for the Stochastic Cahn-Hilliard Equation with Gradient-type Multiplicative Noise