Worst case scenario analysis for elliptic problems with uncertainty

Authors:
I. Babuška;F. Nobile;R. Tempone
Affiliations:
ICES, The University of Texas at Austin, 1 University Station CO200, 78712, TX, USA;MOX, Dipartimento di Matematica, Politecnico di Milano, via Bonardi 9, 20133, Milano, TX, Italy;ICES, The University of Texas at Austin, 1 University Station CO200, 78712, TX, USA
Venue:
Numerische Mathematik
Year:
2005

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Abstract

This work studies linear elliptic problems under uncertainty. The major emphasis is on the deterministic treatment of such uncertainty. In particular, this work uses the Worst Scenario approach for the characterization of uncertainty on functional outputs (quantities of physical interest). Assuming that the input data belong to a given functional set, eventually infinitely dimensional, this work proposes numerical methods to approximate the corresponding uncertainty intervals for the quantities of interest. Numerical experiments illustrate the performance of the proposed methodology.