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Certified error bounds for uncertain elliptic equations

Authors
Journal
Journal of Computational and Applied Mathematics
0377-0427
Publisher
Elsevier
Publication Date
Volume
218
Issue
1
Identifiers
DOI: 10.1016/j.cam.2007.04.037
Keywords
  • Linear Elliptic Partial Differential Equations
  • A Posteriori Error Estimation
  • Dual Weighted Residual (Dwr)
  • Uncertainty Propagation
  • Clouds
Disciplines
  • Mathematics

Abstract

Abstract 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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