Optimal error estimates for linear parabolic problems under minimal regularity assumptions
type: Item
instance of: scholarly article
title: Optimal error estimates for linear parabolic problems under minimal regularity assumptions
zbMATH Open document ID: 0538.65077
DOI: 10.1007/BF02575590
published in: Calcolo
publication date: 1983-01-01T00:00:00Z
review text: The paper deals with error estimates connected with the discretization of a linear parabolic problem \(u_ t+Au=f, u(x,0)=0\) on \(\Omega\), \(u(x,t)=0\) on \(\partial \Omega \times(0,\infty)\) via Galerkin approximation in space and \(\theta\)-method (\(\theta\geq frac{1}{2})\) in time. The error is evaluated in norms of the type \(H_ t^{\delta}(H^ 1_ x)\cap H_ t^{\delta +1/2}(L^ 2_ x)\) for \(| \delta | \leq 1/2\). The derived error estimates are optimal with respect to regularity assumptions on the right-hand side f.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35K20
zbMATH DE Number: 3856349
zbMATH Keywords: optimal error estimates
zbMATH Keywords: Galerkin
zbMATH Keywords: theta-method
zbMATH Keywords: implicit Euler
zbMATH Keywords: Crank- Nicholson
Wikidata QID: Q57386826
author: Claudio Baiocchi
author: Franco Brezzi
reviewed by: Igor Bock
MaRDI profile type: Publication
cites work: Q5661106
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full work available at URL: https://doi.org/10.1007/bf02575590
OpenAlex ID: W2070702139
description: scientific article; zbMATH DE number 3856349