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.
Original language | English |
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Pages (from-to) | 2039-2063 |
Number of pages | 25 |
Journal | SIAM Journal on Numerical Analysis |
Volume | 50 |
Issue number | 4 |
DOIs | |
Publication status | Published - 1 Jan 2012 |