Maximum-norm estimates for finite-element methods for a strongly damped wave equation
type: Item
instance of: scholarly article
title: Maximum-norm estimates for finite-element methods for a strongly damped wave equation
zbMATH Open document ID: 1053.65077
published in: BIT
publication date: 2004-08-06T00:00:00Z
review text: The article refers to earlier work of \textit{S. Larsson, V. Thomée}, and \textit{L. B. Wahlbin}, [IMA J. Numer. Anal. 11, No.~1, 115--142 (1991; Zbl 0718.65070)], which concerns the numerical solution of a homogeneous linear wave equation with strong damping, arising in viscoelasticity. In that work spatial discretization by finite elements and associated fully discrete methods were analyzed in \(L_2\)-based norms. The analysis depended on the fact that the solution may be expressed in terms of an analytic semigroup. In this paper authors combine that approach with recent results on discretization of parabolic problems to derive essentially optimal order error bounds in maximum-norm for piecewise linear finite elements combined with backward Euler and Crank-Nicolson time stepping methods. The error estimates in maximum norm are derived.
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 65M06
zbMATH DE Number: 2081535
zbMATH Keywords: strongly damped wave equation
zbMATH Keywords: finite elements
zbMATH Keywords: error bounds
zbMATH Keywords: semigroup
zbMATH Keywords: resolvent estimate
zbMATH Keywords: maximum-norm
zbMATH Keywords: backward Euler and Crank-Nicolson time stepping methods
author: Vidar Thomée
author: L. B. Wahlbin
reviewed by: Vit Dolejsi
MaRDI profile type: Publication
full work available at URL: b:bitn.0000025091.78408.e4
OpenAlex ID: W2066335031
DOI: 10.1023/B:BITN.0000025091.78408.E4
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description: scientific article; zbMATH DE number 2081535