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Certified error bounds for uncertain elliptic equations

✍ Scribed by Arnold Neumaier

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 340 KB
Volume: 218
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2007.04.037

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✦ Synopsis

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 an energy norm, or of key functionals of the solutions, given an approximate solution. Uncertainty in the parameters specifying the partial differential equations can be taken into account, either in a worst case setting, or given limited probabilistic information in terms of clouds.

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