The h, p and h-p versions of the finite element method in 1 dimension. II. The error analysis of the h- and h-p versions
type: Item
instance of: scholarly article
title: The h, p and h-p versions of the finite element method in 1 dimension. II. The error analysis of the h- and h-p versions
zbMATH Open document ID: 0614.65089
DOI: 10.1007/BF01389734
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: This paper concentrates on h and h-p versions of FEM. Generally, the h- version of FEM has the degree of elements fixed and the convergence is achieved by the refinement of the mesh. The h-p version combines both approaches, the p-version and h-version. The same model problem as in Part I [ibid. 49, 577-612 (1986; reviewed above)] is considered. The paper is mainly concerned with the relation between the relative error in the energy norm and the number of degrees of freedom. The authors show that the selection of the mesh and degree of elements is essential for the performance of the method. More exactly, the proper selection of the h-p version leads to the exponential rate of convergence while the h-version with improper mesh, gives very low algebraic rate when a singularity is present.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 65L50
Mathematics Subject Classification ID: 34B05
zbMATH DE Number: 3994957
zbMATH Keywords: mesh refinement
zbMATH Keywords: finite element method
zbMATH Keywords: h-p versions
zbMATH Keywords: h-version
zbMATH Keywords: convergence
zbMATH Keywords: relative error
zbMATH Keywords: exponential rate of convergence
zbMATH Keywords: singularity
reviewed by: Calin Ioan Gheorghiu
MaRDI profile type: Publication
cites work: The h, p and h-p versions of the finite element method in 1 dimension. I. The error analysis of the p-version
cites work: On optimal global error bounds obtained by scaled local error estimates
description: scientific article; zbMATH DE number 3994957