The \(h,p\) and \(h\)-\(p\) version of the finite element method; basis theory and applications
type: Item
instance of: scholarly article
title: The \(h,p\) and \(h\)-\(p\) version of the finite element method; basis theory and applications
zbMATH Open document ID: 0769.65078
DOI: 10.1016/0965-9978(92)90097-Y
published in: Advances in Engineering Software
publication date: 1993-06-29T00:00:00Z
review text: The paper discusses the fundamental aspects of the three versions of the finite element method with the aim to present the most important facts of the methods that are useful for a better understanding of the results obtained. A simple one-dimensional model problem is considered and the \(h\)-, the \(p\)- and the \(h-p\) versions are explained in detail. Results on the optimal grading of the mesh for a best rate of convergence and the ideas of adaptive mesh construction are described. The authors present results on the features of the \(p\)-version when applied to the model problem, and they discuss some theoretical questions about the \(h- p\) version that give some insight into the desirable mesh design for the \(p\)-version. The authors discuss finally the performance of the \(p\)- and the \(h-p\) version for typical elliptic boundary value problems on polygonal domains especially concerning the singularities of the solution.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 221750
zbMATH Keywords: adaptive methods
zbMATH Keywords: \(h\)-version
zbMATH Keywords: finite element method
zbMATH Keywords: \(h-p\) versions
zbMATH Keywords: best rate of convergence
zbMATH Keywords: adaptive mesh construction
zbMATH Keywords: \(p\)-version
zbMATH Keywords: performance
Wikidata QID: Q56965214
author: Ivo Babuška
author: Benqi Guo
MaRDI profile type: Publication
full work available at URL: 0965-9978(92)90097-y
OpenAlex ID: W2028526482
description: scientific article; zbMATH DE number 221750