Numerical analysis for semilinear evolution equations of parabolic type.
type: Item
instance of: scholarly article
title: Numerical analysis for semilinear evolution equations of parabolic type.
zbMATH Open document ID: 1034.65040
DOI: 10.1016/S0377-0427(03)00567-3
author: Etsushi Nakaguchi
author: Atsushi Yagi
published in: Journal of Computational and Applied Mathematics
publication date: 2003-10-15T00:00:00Z
review text: The full discretization of a semilinear abstract evolution equation of parabolic type is considered. The time discretization is carried out by an Euler scheme that is implicit in the main part but explicit in the semilinear part. The spatial approximation is based upon a Galerkin method. The authors derive stability and error estimates by employing the semigroup approach as well as energy techniques. Although the results are rather known, it is nice to have this comparison of the two major approaches.
reviewed by: Etienne Emmrich
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35K90
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M15
zbMATH DE Number: 1993203
zbMATH Keywords: semilinear evolution equation
zbMATH Keywords: Galerkin method
zbMATH Keywords: Euler time discretization
zbMATH Keywords: semigroup approach
zbMATH Keywords: variational method
zbMATH Keywords: stability estimate
zbMATH Keywords: error estimate
zbMATH Keywords: comparison of methods
zbMATH Keywords: energy techniques
MaRDI profile type: Publication
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full work available at URL: s0377-0427(03)00567-3
OpenAlex ID: W2066096365
description: scientific article; zbMATH DE number 1993203