Efficient computable error bounds for discontinuous Galerkin approximations of elliptic problems
type: Item
instance of: scholarly article
title: Efficient computable error bounds for discontinuous Galerkin approximations of elliptic problems
zbMATH Open document ID: 1163.65077
published in: Journal of Computational and Applied Mathematics
publication date: 2009-03-30T00:00:00Z
review text: The authors present guaranteed and computable both sided error bounds for the discontinuous Galerkin (DG) approximations of elliptic problems. These estimates are derived in the full DG-norm on purely functional grounds by the analysis of the respective differential problem, and thus, are applicable to any qualified DG approximation. Based on the triangle inequality, the underlying approach has the following steps for a given DG approximation: (1) computing a conforming approximation in the energy space using the Oswald interpolation operator, and (2) application of the existing functional a posteriori error estimates to the conforming approximation. Various numerical examples with varying difficulty in computing the error bounds, from simple problems of polynomial-type analytic solution to problems with analytic solution having sharp peaks, or problems with jumps in the coefficients of the partial differential equation operator, are presented which confirm the efficiency and the robustness of the estimates.
reviewed by: Wilhelm Heinrichs
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35R05
zbMATH DE Number: 5534939
zbMATH Keywords: a posteriori error estimates
zbMATH Keywords: discontinuous Galerkin method
zbMATH Keywords: elliptic partial differential equation
zbMATH Keywords: numerical examples
zbMATH Keywords: problems with jumps in the coefficients
author: S. K. Tomar
author: Sergey Repin
MaRDI profile type: Publication
full work available at URL: j.cam.2008.08.015
OpenAlex ID: W2034957063
Wikidata QID: Q110085182
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DOI: 10.1016/J.CAM.2008.08.015
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description: scientific article; zbMATH DE number 5534939