Backward Euler method for abstract time-dependent parabolic equations with variable domains
type: Item
instance of: scholarly article
title: Backward Euler method for abstract time-dependent parabolic equations with variable domains
zbMATH Open document ID: 0936.65107
published in: Numerische Mathematik
publication date: 1999-11-01T00:00:00Z
review text: For linear parabolic problems with time-dependent operator, the temporal discretization by means of the implicit Euler method is studied in an abstract Banach space setting. This covers also problems with time-dependent non-homogeneous right-hand side and boundary conditions. The author proves new general results in the situation of operators with time-dependent domain of definition. Error estimates are obtained for sufficiently smooth exact solutions and operators being Hölder continuous. Finally, the author shows how classical problems meet the new framework.
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65J10
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 1356179
zbMATH Keywords: time discretization
zbMATH Keywords: backward Euler method
zbMATH Keywords: error estimates
zbMATH Keywords: linear parabolic problems
zbMATH Keywords: implicit Euler method
zbMATH Keywords: Banach space
author: César Palencia
reviewed by: Etienne Emmrich
MaRDI profile type: Publication
full work available at URL: s002110050427
OpenAlex ID: W2056399022
DOI: 10.1007/S002110050427
description: scientific article; zbMATH DE number 1356179