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On the convergence of generalized polynomial chaosexpansions

Published online by Cambridge University Press:  12 October 2011

Oliver G. Ernst ,
Antje Mugler ,
Hans-Jörg Starkloff  and
Elisabeth Ullmann
Oliver G. Ernst
Affiliation:
Institut für Numerische Mathematik und Optimierung, TU Bergakademie Freiberg, 09596 Freiberg, Germany. ernst@math.tu-freiberg.de; ullmann@math.tu-freiberg.de
Antje Mugler
Affiliation:
Fachgruppe Mathematik, University of Applied Sciences Zwickau, 08012 Zwickau, Germany; Antje.Mugler@fh-zwickau.de; hans.joerg.starkloff@fh-zwickau.de
Hans-Jörg Starkloff
Affiliation:
Fachgruppe Mathematik, University of Applied Sciences Zwickau, 08012 Zwickau, Germany; Antje.Mugler@fh-zwickau.de; hans.joerg.starkloff@fh-zwickau.de
Elisabeth Ullmann
Affiliation:
Institut für Numerische Mathematik und Optimierung, TU Bergakademie Freiberg, 09596 Freiberg, Germany. ernst@math.tu-freiberg.de; ullmann@math.tu-freiberg.de
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Abstract

A number of approaches for discretizing partial differential equations with random dataare based on generalized polynomial chaos expansions of random variables. These constitutegeneralizations of the polynomial chaos expansions introduced by Norbert Wiener toexpansions in polynomials orthogonal with respect to non-Gaussian probability measures. Wepresent conditions on such measures which imply mean-square convergence of generalizedpolynomial chaos expansions to the correct limit and complement these with illustrativeexamples.

Keywords

Equations with random datapolynomial chaosgeneralized polynomial chaosWiener–Hermite expansionWiener integraldeterminate measuremoment problemstochastic Galerkin methodspectral elements
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 2 , March 2012 , pp. 317 - 339
Copyright
© EDP Sciences, SMAI, 2011

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