Stability and analyticity in maximum-norm for simplical Lagrange finite element semidiscretizations of parabolic equations with Dirichlet boundary conditions
type: Item
instance of: scholarly article
title: Stability and analyticity in maximum-norm for simplical Lagrange finite element semidiscretizations of parabolic equations with Dirichlet boundary conditions
zbMATH Open document ID: 0973.65079
published in: Numerische Mathematik
publication date: 2001-01-16T00:00:00Z
review text: By the authors' abstract: Stability and analyticity estimates in maximum-norm are shown for spatially discrete finite element approximations based on simplicial Lagrange elements for the model heat equation with homogeneous Dirichlet boundary conditions. By assumption, the family of partitions is quasiuniform. The bounds are logarithm free and valid in arbitrary dimension and for arbitrary polynomial degree. The work continues an earlier study by \textit{A. H. Schatz}, \textit{V. Thomée}, and \textit{L. B. Wahlbin} [Commun. Pure Appl. Math. 51, No. 11-12, 1349-1385 (1998; Zbl 0932.65103)] in which Neumann boundary conditions were considered.
reviewed by: Pavel Burda
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 1552925
zbMATH Keywords: semidiscretizations
zbMATH Keywords: finite element method
zbMATH Keywords: parabolic equation
zbMATH Keywords: stability
zbMATH Keywords: heat equation
author: Vidar Thomée
author: L. B. Wahlbin
MaRDI profile type: Publication
full work available at URL: s002110000184
OpenAlex ID: W1984477528
DOI: 10.1007/S002110000184
description: scientific article; zbMATH DE number 1552925