Shadowing for discrete approximations of abstract parabolic equations
type: Item
instance of: scholarly article
title: Shadowing for discrete approximations of abstract parabolic equations
zbMATH Open document ID: 1158.65066
author: Wolf-Jürgen Beyn
author: S. I. Piskarev
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2008-07-21T00:00:00Z
review text: The paper deals with the analysis of a rather general semi-discretization schemes (i.e. with continuous \(t\)) for the nonlinear problem \[ u^{\prime}(t)=Au(t)+f(u(t)), \quad u(0)=u^{0}, \] where \(A\) is an operator coefficient in a Banach space. The authors prove a shadowing theorem which compares the exact and the semi-discrete solutions.The main assumptions can be verified for operators with compact resolvents and for wide classes of the finite-element as well as finite difference discretizations.
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35K90
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 47J35
zbMATH DE Number: 5302650
zbMATH Keywords: abstract nonlinear parabolic problem
zbMATH Keywords: Banach space
zbMATH Keywords: finite-element discretization
zbMATH Keywords: finite-difference discretization
zbMATH Keywords: semi-discretization scheme
zbMATH Keywords: shadowing
reviewed by: Iwan Gawriljuk
MaRDI profile type: Publication
full work available at URL: dcdsb.2008.10.19
OpenAlex ID: W2324420703
DOI: 10.3934/DCDSB.2008.10.19
description: scientific article; zbMATH DE number 5302650