On the Galerkin finite element approximations to multi-dimensional differential and integro-differential parabolic equations
type: Item
instance of: scholarly article
title: On the Galerkin finite element approximations to multi-dimensional differential and integro-differential parabolic equations
zbMATH Open document ID: 0876.65092
DOI: 10.1007/BF02510212
published in: BIT
publication date: 1997-08-24T00:00:00Z
review text: The semidiscretization of differential and integro-differential equations of parabolic type with up to three spatial dimensions by means of a Galerkin finite element method is considered. The author proves error estimates in the maximum norm by using the operator method. These estimates are of optimal or almost optimal order in the case of simplicial Lagrangian polynomial elements. With the paper in hand, earlier results that provide error analysis in the \(L_2\)-norm or for the case of a time-independent elliptic operator are extended.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65M12
zbMATH DE Number: 1033759
zbMATH Keywords: semidiscretization
zbMATH Keywords: integro-differential equations
zbMATH Keywords: parabolic type
zbMATH Keywords: Galerkin finite element method
zbMATH Keywords: error estimates
zbMATH Keywords: operator method
author: Nikolai Yu. Bakaev
reviewed by: Etienne Emmrich
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02510212
OpenAlex ID: W2143432837
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description: scientific article; zbMATH DE number 1033759