Error analysis for Laplace transform - finite element solution of hyperbolic equations
type: Item
instance of: scholarly article
title: Error analysis for Laplace transform - finite element solution of hyperbolic equations
zbMATH Open document ID: 0544.65079
DOI: 10.1007/BF01396305
author: Jozef Brilla
published in: Numerische Mathematik
publication date: 1983-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/132839
review text: The finite element method with Laplace transform of the time variable for the hyperbolic problem \(u_{tt}+A(x)u(x,t)=q(x,t), (x,t)\in \Omega \times(0,\infty), A(x)=\sum_{| \alpha | =| \beta | =m}(-1)^{| \alpha |}D^{\alpha}a_{\alpha \beta}(x)D^{\beta}, \partial^ ju/\partial n^ j=0, (x,t)\in \partial \Omega \times(0,\infty),\) 0\(\leq j\leq m-1\), \(u(x,0)=u_ 0(x)\), \(u_ t(x,0)=u_ 1(x)\), \(x\in {\bar \Omega}\), is analysed. Error estimates in Hardy spaces \(L_ 2\quad(R^+,H^ m,\sigma), \sigma>0\), with weight \(e^{-2\sigma t}\) are derived.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35A22
Mathematics Subject Classification ID: 35L35
zbMATH DE Number: 3866526
zbMATH Keywords: finite element method
zbMATH Keywords: Laplace transform
zbMATH Keywords: error estimates in Hardy spaces
zbMATH Keywords: weighted Hilbert spaces
reviewed by: Igor Bock
MaRDI profile type: Publication
cites work: Q5518037
cites work: Finite Element Method in Linear Viscoelasticity
cites work: A Laplace transform calculus for partial differential operators
cites work: Q4104278
OpenAlex ID: W2042900699
description: scientific article; zbMATH DE number 3866526