Error Estimates of Semidiscrete and Fully Discrete Finite Element Methods for the Cahn--Hilliard--Cook equation

DOI10.1137/19M1259183MaRDI QIDQ5113124

Xiao-Jie Wang, Rui-sheng Qi

Publication date: 10 June 2020

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.10921

zbMATH Keywords

finite element methodbackward Euler methodCahn-Hilliard-Cook equationstrong convergence rates

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (10)

Strong convergence rates of an explicit scheme for stochastic Cahn-Hilliard equation with additive noise ⋮ Finite element approximation of the linearized stochastic Cahn-Hilliard equation with fractional Brownian motion ⋮ Weak convergence of the backward Euler method for stochastic Cahn-Hilliard equation with additive noise ⋮ Strong convergence rates for the approximation of a stochastic time-fractional Allen-Cahn equation ⋮ Strong convergence for an explicit fully‐discrete finite element approximation of the Cahn‐Hillard‐Cook equation with additive noise ⋮ Stability and convergence analysis of a fully discrete semi-implicit scheme for stochastic Allen-Cahn equations with multiplicative noise ⋮ Absolute continuity and numerical approximation of stochastic Cahn-Hilliard equation with unbounded noise diffusion ⋮ Optimal error estimates of Galerkin finite element methods for stochastic Allen-Cahn equation with additive noise ⋮ \(L^p\)-convergence rate of backward Euler schemes for monotone SDEs ⋮ Strong Convergence of a Fully Discrete Scheme for Multiplicative Noise Driving SPDEs with Non-Globally Lipschitz Continuous Coefficients

Cites Work

• Unnamed Item
• An unconditionally energy stable finite difference scheme for a stochastic Cahn-Hilliard equation
• Strong and weak approximation of semilinear stochastic evolution equations
• Optimal strong rates of convergence for a space-time discretization of the stochastic Allen-Cahn equation with multiplicative noise
• Strong convergence rates for nonlinearity-truncated Euler-type approximations of stochastic Ginzburg-Landau equations
• On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients
• Exponential moments for numerical approximations of stochastic partial differential equations
• Optimal error estimates of Galerkin finite element methods for stochastic Allen-Cahn equation with additive noise
• Analysis of some splitting schemes for the stochastic Allen-Cahn equation
• Convergence of tamed Euler schemes for a class of stochastic evolution equations
• An Introduction to Computational Stochastic PDEs
• On the Backward Euler Approximation of the Stochastic Allen-Cahn Equation
• Finite Element Methods for the Stochastic Allen--Cahn Equation with Gradient-type Multiplicative Noise
• Finite-element approximation of the linearized Cahn-Hilliard-Cook equation
• Finite Element Approximation of the Cahn–Hilliard–Cook Equation
• Error Estimates with Smooth and Nonsmooth Data for a Finite Element Method for the Cahn-Hilliard Equation
• Strong Convergence of a Fully Discrete Finite Element Approximation of the Stochastic Cahn--Hilliard Equation
• On the discretisation in time of the stochastic Allen–Cahn equation
• Stochastic Cahn-Hilliard equation
• Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities
• Strong approximation of monotone stochastic partial differential equations driven by white noise
• Stochastic Equations in Infinite Dimensions
• Erratum: Finite Element Approximation of the Cahn--Hilliard--Cook Equation
• Free Energy of a Nonuniform System. I. Interfacial Free Energy
• Strong and Weak Convergence Rates of a Spatial Approximation for Stochastic Partial Differential Equation with One-sided Lipschitz Coefficient
• Strong convergence rates of semidiscrete splitting approximations for the stochastic Allen–Cahn equation
• Galerkin Finite Element Methods for Parabolic Problems
• Finite-Element Methods for a Strongly Damped Wave Equation
• Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations

This page was built for publication: Error Estimates of Semidiscrete and Fully Discrete Finite Element Methods for the Cahn--Hilliard--Cook equation