The h, p and h-p versions of the finite element method in 1 dimension. I. The error analysis of the p-version
type: Item
instance of: scholarly article
title: The h, p and h-p versions of the finite element method in 1 dimension. I. The error analysis of the p-version
zbMATH Open document ID: 0614.65088
DOI: 10.1007/BF01389733
author: Yanyan Li
published in: Numerische Mathematik
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133132
review text: The p-version of the finite element method fixes the mesh and the convergence is obtained by increase of the degree of elements. This paper realizes an error analysis of this FEM version considering the most simple one-dimensional bilocal problem when its solution has a singularity of \(x^{\alpha}\)-type. The analysis is made in the more general frame of the best \(L_ 2\)-approximation of analytic functions which have a singularity of this type. Some numerical results confirm the accuracy of the estimates and show the performance of the p-version.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 34B05
zbMATH DE Number: 3994956
zbMATH Keywords: singular solution
zbMATH Keywords: finite element method
zbMATH Keywords: convergence
zbMATH Keywords: error analysis
zbMATH Keywords: bilocal problem
zbMATH Keywords: p-version
reviewed by: Calin Ioan Gheorghiu
MaRDI profile type: Publication
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OpenAlex ID: W2792013640
description: scientific article; zbMATH DE number 3994956