A priori error analysis of stochastic Galerkin mixed approximations of elliptic PDEs with random data

Bespalov, Alexei and Powell, Catherine E. and Silvester, David (2012) A priori error analysis of stochastic Galerkin mixed approximations of elliptic PDEs with random data. SIAM Journal on Numerical Analysis, 50 (4). pp. 2039-2063. ISSN 1095-7170

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Official URL: http://dx.doi.org/10.1137/110854898

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.

Item Type: Article
Uncontrolled Keywords: mixed finite elements, saddle point problems, stochastic finite elements, random data, Karhunen-Loeve expansion, a priori analysis, error estimates
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Alex Bespalov
Date Deposited: 10 Nov 2011
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1696

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