ON THE CONVERGENCE OF GENERALIZED POLYNOMIAL CHAOS EXPANSIONS

被引：276
|
作者：
Ernst, Oliver G. [1 ]
Mugler, Antje [2 ]
Starkloff, Hans-Joerg [2 ]
Ullmann, Elisabeth [1 ]
机构：
[1] TU Bergakad Freiberg, Inst Numer Math & Optimierung, D-09596 Freiberg, Germany
[2] Univ Appl Sci Zwickau, Fachgrp Math, D-08012 Zwickau, Germany
来源：
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS | 2012年 / 46卷 / 02期
关键词：
Equations with random data; polynomial chaos; generalized polynomial chaos; Wiener-Hermite expansion; Wiener integral; determinate measure; moment problem; stochastic Galerkin method; spectral elements; DIFFERENTIAL-EQUATIONS; MODELING UNCERTAINTY; ELEMENT-METHOD; FLOW; REPRESENTATIONS; APPROXIMATIONS;
D O I：
10.1051/m2an/2011045
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：317 / 339
页数：23
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