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2011.91: A priori error analysis of stochastic Galerkin mixed approximations of elliptic PDEs with random data

2011.91: Alexei Bespalov, Catherine E. Powell and David Silvester (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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DOI: 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 2000 > 35 Partial differential equations
MSC 2000 > 65 Numerical analysis
MIMS number:2011.91
Deposited By:Alex Bespalov
Deposited On:10 November 2011

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