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A Priori Error Analysis of Stochastic Galerkin Mixed Approximations of Elliptic PDEs with Random Data

Alexei Bespalov and Catherine E. Powell and David Silvester

SIAM Journal on Numerical Analysis. 2012;50(4):2039-2063.

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Abstract

We construct stochastic Galerkin approximations to the solution of a first-order system of PDEs with random coefficients. Under the standard finite-dimensional noise assumption, we transform the variational saddle point problem to a parametric deterministic one. Approximations are constructed by combining mixed finite elements on the computational domain with $M$-variate tensor product polynomials. We study the inf-sup stability and well-posedness of the continuous and finite-dimensional problems, the regularity of solutions with respect to the $M$ parameters describing the random coefficients, and establish a priori error estimates for stochastic Galerkin finite element approximations.

Bibliographic metadata

Type of resource:
Content type:
Publication type:
Publication form:
Published date:
Volume:
50
Issue:
4
Start page:
2039
End page:
2063
Pagination:
25
Digital Object Identifier:
10.1137/110854898
Access state:
Active

Institutional metadata

University researcher(s):

Record metadata

Manchester eScholar ID:
uk-ac-man-scw:172638
Created by:
Silvester, David
Created:
2nd October, 2012, 16:13:04
Last modified by:
Silvester, David
Last modified:
11th March, 2014, 21:19:47