Interpolation error-based a posteriori error estimation for \(hp\)-refinement using first and second derivative jumps.
type: Item
instance of: scholarly article
title: Interpolation error-based a posteriori error estimation for \(hp\)-refinement using first and second derivative jumps.
zbMATH Open document ID: 1080.65108
author: Peter K. Moore
published in: Applied Numerical Mathematics
publication date: 2004-01-26T00:00:00Z
review text: This demanding paper presents relevant new results concerning the a posteriori error estimation for the \(hp\)-adaptive finite-element method. These results can be used to optimise the \(hp\)-adaptive refinement process. After introducing the reader into the treated subject, the needed function-analytical framework and assumptions are settled. In the following the Lobatto polynomials together with some facts concerning their interpolational properties are given. Using a Taylor like expansion of the interpolation error, relations between jumps of the first and second derivative of the interpolant and the finite-element-solution, obtained with a \(p\)-order increased by one respectively increased by two, are derived. The strong assumption for these results, namely uniform meshes, are in the following alleviated to the assumption of uniform \(p\)-order. The paper includes also computational results comparing the newly derived estimates with those obtained by earlier approaches together with a discussion of the impact of the presented results on the \(hp\)-refinement strategy.
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65N50
zbMATH DE Number: 2033027
zbMATH Keywords: A posteriori error estimation
zbMATH Keywords: hp-adaptive refinement
zbMATH Keywords: error bounds
zbMATH Keywords: finite-element method
reviewed by: Hermann G. Matthies
MaRDI profile type: Publication
full work available at URL: j.apnum.2003.06.001
OpenAlex ID: W2022488045
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DOI: 10.1016/J.APNUM.2003.06.001
description: scientific article; zbMATH DE number 2033027