| Issue |
ESAIM: M2AN
Volume 46, Number 2, November-December 2012
|
|
|---|---|---|
| Page(s) | 317 - 339 | |
| DOI | https://doi.org/10.1051/m2an/2011045 | |
| Published online | 12 October 2011 | |
On the convergence of generalized polynomial chaos expansions
1
Institut für Numerische Mathematik und Optimierung,
TU Bergakademie Freiberg,
09596
Freiberg,
Germany
ernst@math.tu-freiberg.de; ullmann@math.tu-freiberg.de
2
Fachgruppe Mathematik, University of Applied Sciences
Zwickau, 08012
Zwickau,
Germany
Antje.Mugler@fh-zwickau.de;
hans.joerg.starkloff@fh-zwickau.de
Received:
18
January
2011
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.