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Title: Adaptive algorithm for stochastic Galerkin method (English)
Author: Pultarová, Ivana
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 60
Issue: 5
Year: 2015
Pages: 551-571
Summary lang: English
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Category: math
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Summary: We introduce a new tool for obtaining efficient a posteriori estimates of errors of approximate solutions of differential equations the data of which depend linearly on random parameters. The solution method is the stochastic Galerkin method. Polynomial chaos expansion of the solution is considered and the approximation spaces are tensor products of univariate polynomials in random variables and of finite element basis functions. We derive a uniform upper bound to the strengthened Cauchy-Bunyakowski-Schwarz constant for a certain hierarchical decomposition of these spaces. Based on this, an adaptive algorithm is proposed. A simple numerical example illustrates the efficiency of the algorithm. Only the uniform distribution of random variables is considered in this paper, but the results obtained can be modified to any other type of random variables. (English)
Keyword: stochastic Galerkin method
Keyword: a posteriori error estimate
Keyword: strengthened Cauchy-Bunyakowski-Schwarz constant
Keyword: adaptive refinement
MSC: 65C20
MSC: 65N22
idZBL: Zbl 06486925
idMR: MR3396480
DOI: 10.1007/s10492-015-0111-9
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Date available: 2015-09-03T10:43:31Z
Last updated: 2020-01-05
Stable URL: http://hdl.handle.net/10338.dmlcz/144391
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