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期刊名称: Acta Numerica
Volume:23    Page:521-650
ISSN:0962-4929

Stochastic finite element methods for partial differential equations with random input data期刊论文

作者: Gunzburger Max D Webster Clayton G Zhang Guannan
DOI:10.1017/S0962492914000075

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页码: 521-650
被引频次: 55
出版者: CAMBRIDGE UNIV PRESS,Cambridge University Press
期刊名称: Acta Numerica
ISSN: 0962-4929
语言: English
摘要: The quantification of probabilistic uncertainties in the outputs of physical, biological, and social systems governed by partial differential equations with random inputs require, in practice, the discretization of those equations. Stochastic finite element methods refer to an extensive class of algorithms for the approximate solution of partial differential equations having random input data, for which spatial discretization is effected by a finite element method. Fully discrete approximations require further discretization with respect to solution dependences on the random variables. For this purpose several approaches have been developed, including intrusive approaches such as stochastic Galerkin methods, for which the physical and probabilistic degrees of freedom are coupled, and non-intrusive approaches such as stochastic sampling and interpolatory-type stochastic collocation methods, for which the physical and probabilistic degrees of freedom are uncoupled. All these method classes are surveyed in this article, including some novel recent developments. Details about the construction of the various algorithms and about theoretical error estimates and complexity analyses of the algorithms are provided. Throughout, numerical examples are used to illustrate the theoretical results and to provide further insights into the methodologies.
相关主题: MATHEMATICS, ELLIPTIC PROBLEMS, COLLOCATION METHOD, RANDOM-MATRIX THEORY, UNCERTAINTY QUANTIFICATION, ERROR ANALYSIS, BOUNDARY-VALUE-PROBLEMS, PROBABILISTIC COLLOCATION, MODELING UNCERTAINTY, DOMAIN DECOMPOSITION, CENTROIDAL VORONOI TESSELLATION, Probability, Uncertainty, Stochastic models, Finite element analysis, Partial differential equations,

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