On the convergence of generalized polynomial chaos expansions

Oliver G. Ernst; Antje Mugler; Hans-Jörg Starkloff; Elisabeth Ullmann

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

  • Volume: 46, Issue: 2, page 317-339
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Ernst, Oliver G., et al. "On the convergence of generalized polynomial chaos expansions." ESAIM: Mathematical Modelling and Numerical Analysis 46.2 (2011): 317-339. <http://eudml.org/doc/222104>.

@article{Ernst2011,
abstract = {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.},
author = {Ernst, Oliver G., Mugler, Antje, Starkloff, Hans-Jörg, Ullmann, Elisabeth},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Equations with random data; polynomial chaos; generalized polynomial chaos; Wiener–Hermite expansion; Wiener integral; determinate measure; moment problem; stochastic Galerkin method; spectral elements; equations with random data; Wiener-Hermite expansion; numerical examples},
language = {eng},
month = {10},
number = {2},
pages = {317-339},
publisher = {EDP Sciences},
title = {On the convergence of generalized polynomial chaos expansions},
url = {http://eudml.org/doc/222104},
volume = {46},
year = {2011},
}

TY - JOUR
AU - Ernst, Oliver G.
AU - Mugler, Antje
AU - Starkloff, Hans-Jörg
AU - Ullmann, Elisabeth
TI - On the convergence of generalized polynomial chaos expansions
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2011/10//
PB - EDP Sciences
VL - 46
IS - 2
SP - 317
EP - 339
AB - 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.
LA - eng
KW - Equations with random data; polynomial chaos; generalized polynomial chaos; Wiener–Hermite expansion; Wiener integral; determinate measure; moment problem; stochastic Galerkin method; spectral elements; equations with random data; Wiener-Hermite expansion; numerical examples
UR - http://eudml.org/doc/222104
ER -

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