Volume 46, Number 2, November-December 2012
|Page(s)||317 - 339|
|Published online||12 October 2011|
On the convergence of generalized polynomial chaos expansions
Institut für Numerische Mathematik und Optimierung,
TU Bergakademie Freiberg,
2 Fachgruppe Mathematik, University of Applied Sciences Zwickau, 08012 Zwickau, Germany
A number of approaches for discretizing partial differential equations with random data are based on generalized polynomial chaos expansions of random variables. These constitute generalizations of the polynomial chaos expansions introduced by Norbert Wiener to expansions in polynomials orthogonal with respect to non-Gaussian probability measures. We present conditions on such measures which imply mean-square convergence of generalized polynomial chaos expansions to the correct limit and complement these with illustrative examples.
Mathematics Subject Classification: 33C45 / 35R60 / 40A30 / 41A10 / 60H35 / 65N30
Key words: Equations with random data / polynomial chaos / generalized polynomial chaos / Wiener–Hermite expansion / Wiener integral / determinate measure / moment problem / stochastic Galerkin method / spectral elements
© EDP Sciences, SMAI, 2011
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