Condition number and diagonal preconditioning: Comparison of the \(p\)-version and the spectral element methods
type: Item
instance of: scholarly article
title: Condition number and diagonal preconditioning: Comparison of the \(p\)-version and the spectral element methods
zbMATH Open document ID: 0858.65114
author: Olivier Pourquier
author: Jean-François Maitre
published in: Numerische Mathematik
publication date: 1997-03-11T00:00:00Z
review text: For adaptive schemes the hierarchical basis is used in the \(p\)-version of the finite element method. The condition number for the matrices of the commonly used basis introduced by \textit{I. Babuška} and \textit{B. A. Szabo} [Finite element analysis (1991; Zbl 0792.73003)] is investigated. For \(d\)-dimensional rectangular elements it is shown that the condition number is equivalent to \(p^{4(d-1)}\) and to \(p^{4d}\) for the stiffness and the mass matrix. Moreover, the usual diagonal preconditioning divides in the previous orders the exponents of \(p\) by two. The results are compared to those obtained for spectral elements.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 932009
zbMATH Keywords: spectral element methods
zbMATH Keywords: \(p\)-version
zbMATH Keywords: hierarchical basis
zbMATH Keywords: finite element method
zbMATH Keywords: condition number
zbMATH Keywords: diagonal preconditioning
reviewed by: Wilhelm Heinrichs
MaRDI profile type: Publication
full work available at URL: s002110050208
OpenAlex ID: W2064037951
DOI: 10.1007/S002110050208
description: scientific article; zbMATH DE number 932009