Year: 2011
Type: report
Abstract: It is common practice in the study of stochastic Galerkin methods for boundary value problems depending on random fields to truncate a series representation of this field prior to the Galerkin discretization. We show that this is unnecessary; the projection onto a finite dimensional subspace automatically replaces the infinite series expansion by a suitable partial sum. We construct tensor product polynomial bases on infinite dimensional parameter domains, and use these to recast a random boundary value problem as a countably infinite system of deterministic equations. The stochastic Galerkin method can be interpreted as a standard finite element discretization of a finite section of this infinite system.
Author: Gittelson, Claude Jeffrey
Language: English
Subfield: Statistics, Probability and Uncertainty
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W2155962491