An asymptotically exact, pointwise, a posteriori error estimator for linear, elliptic, one-dimensional problems with possible singularities in the solution
type: Item
instance of: scholarly article
title: An asymptotically exact, pointwise, a posteriori error estimator for linear, elliptic, one-dimensional problems with possible singularities in the solution
zbMATH Open document ID: 0819.65112
DOI: 10.1016/0377-0427(94)90177-5
author: Jens Hugger
published in: Journal of Computational and Applied Mathematics
publication date: 1995-09-05T00:00:00Z
review text: This paper deals with the finite element solution of a variational problem which possesses certain superconvergence properties. It is possible to obtain a correction term providing an additional order of approximation of the solution. The correction can be used for error estimation locally or globally. Here a correction term is found with the convergence properties in the special case of one-dimensional linear elliptic problems. The author gives special attention to the effects of the appearance of singularities and zeros of derivatives in the exact solution. Some computational results are included.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 34B05
zbMATH DE Number: 739553
zbMATH Keywords: numerical examples
zbMATH Keywords: finite element
zbMATH Keywords: superconvergence
zbMATH Keywords: error estimation
zbMATH Keywords: linear elliptic problems
zbMATH Keywords: singularities
zbMATH Keywords: zeros of derivatives
reviewed by: Pavol Chocholatý
MaRDI profile type: Publication
full work available at URL: 0377-0427(94)90177-5
OpenAlex ID: W2080514488
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description: scientific article; zbMATH DE number 739553