Certified error bounds for uncertain elliptic equations
type: Item
instance of: scholarly article
title: Certified error bounds for uncertain elliptic equations
zbMATH Open document ID: 1145.65088
published in: Journal of Computational and Applied Mathematics
publication date: 2008-07-01T00:00:00Z
review text: In many applications, partial differential equations depend on parameters which are only approximately known. Using tools from functional analysis and global optimization, methods are presented for obtaining certificates for rigorous and realistic error bounds on the solution of linear elliptic partial differential equations in arbitrary domains, either in the energy norm, or of key functionals of the solution. Uncertainty in the parameters can be taken into account, either in a worst case setting, or given limited probalistic information in terms of clouds.
reviewed by: Wilhelm Heinrichs
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 5295237
zbMATH Keywords: linear elliptic partial differential equations
zbMATH Keywords: a posteriori error estimation
zbMATH Keywords: dual weighted residual
zbMATH Keywords: uncertainty propagation
zbMATH Keywords: clouds
author: Arnold Neumaier
describes a project that uses: PENNON
describes a project that uses: NEOS
describes a project that uses: AMPL
describes a project that uses: INTOPT_90
MaRDI profile type: Publication
full work available at URL: j.cam.2007.04.037
OpenAlex ID: W2154529597
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DOI: 10.1016/J.CAM.2007.04.037
description: scientific article; zbMATH DE number 5295237