A numerical analysis of the Cahn-Hilliard equation with dynamic boundary conditions
type: Item
instance of: scholarly article
title: A numerical analysis of the Cahn-Hilliard equation with dynamic boundary conditions
zbMATH Open document ID: 1204.65113
author: Laurence Cherfils
author: Mădălina Petcu
author: Morgan Pierre
published in: Discrete and Continuous Dynamical Systems
publication date: 2010-06-23T00:00:00Z
review text: A finite element space semi-discretization of the Cahn-Hilliard equation with dynamic boundary conditions has been studied. Optimal error estimates in energy and weaker norms have been proved for sufficiently regular solutions. A convergence result in a weak sense for less regular solutions has also been proved. A fully discrete scheme based on the backward Euler scheme for the time discretization has been proposed and proved to be unconditionally stable. Some numerical examples are presented.
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 65M15
zbMATH DE Number: 5725445
zbMATH Keywords: finite element method
zbMATH Keywords: error estimates
zbMATH Keywords: backward Euler scheme
zbMATH Keywords: linearized Crank-Nicolson scheme
zbMATH Keywords: semilinear parabolic problem
zbMATH Keywords: Łojasiewicz inequality
zbMATH Keywords: semi-discretization
zbMATH Keywords: Cahn-Hilliard equation
zbMATH Keywords: convergence
zbMATH Keywords: numerical examples
reviewed by: Dinh Nho Hào
MaRDI profile type: Publication
full work available at URL: dcds.2010.27.1511
OpenAlex ID: W1971626990
DOI: 10.3934/DCDS.2010.27.1511
description: scientific article; zbMATH DE number 5725445