I. Babu²ka, F. Nobile, and R. Tempone, A stochastic collocation method for elliptic partial dierential equations with random input data, SIAM J. Numer. Anal, vol.45, issue.3, p.10051034, 2007.

I. Babu²ka, R. Tempone, and G. E. Zouraris, Galerkin nite element approximations of stochastic elliptic partial dierential equations, SIAM J. Numer. Anal, vol.42, issue.2, p.800825, 2004.

F. Espen-benth and J. Gjerde, Convergence rates for nite element approximations of stochastic partial dierential equations, Stochastics Stochastics Rep, vol.63, pp.3-4313, 1998.

M. Bieri and C. Schwab, Sparse high order FEM for elliptic sPDEs, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.13-14, pp.13-1411491170, 2009.
DOI : 10.1016/j.cma.2008.08.019

G. Da, P. , and J. Zabczyk, Stochastic equations in innite dimensions, volume 44 of Encyclopedia of Mathematics and its Applications, 1992.

A. M. Stuart and M. Dashti, Uncertainty quantication and weak approximation of an elliptic inverse problem. submitted, 2010.

P. Frauenfelder, C. Schwab, and R. Todor, Finite elements for elliptic problems with stochastic coecients, Comput. Methods Appl. Mech. Engrg, vol.194, issue.25, p.205228, 2005.

J. Galvis and M. Sarkis, Approximating innity-dimensional stochastic Darcy's equations without uniform ellipticity, SIAM J. Numer. Anal, vol.47, issue.5, p.36243651, 2009.

B. Ganis, H. Klie, M. F. Wheeler, T. Wildey, I. Yotov et al., Stochastic collocation and mixed nite elements for ow in porous media

R. G. Ghanem and P. D. Spanos, Spectral techniques for stochastic nite elements, Arch. Comput. Methods Engrg, vol.4, issue.1, p.63100, 1997.
DOI : 10.1007/bf02818931

R. Ghanem and J. Red-horse, Propagation of probabilistic uncertainty in complex physical systems using a stochastic nite element approach, Phys. D, vol.133, pp.1-4137

G. Roger, P. D. Ghanem, and . Spanos, Stochastic nite elements: a spectral approach

C. J. Gittelson, Stochastic Galerkin discretization of the log-normal isotropic diusion problem, Math. Models Methods Appl. Sci, vol.20, issue.2, p.237263, 2010.

E. Hille, Contributions to the theory of Hermitian series. II. The representation problem, Trans. Amer. Math. Soc, vol.47, p.8094, 1940.

O. P. Le-maître, O. M. Knio, H. N. Najm, and R. G. Ghanem, Uncertainty propagation using Wiener???Haar expansions, Journal of Computational Physics, vol.197, issue.1, p.2857, 2004.
DOI : 10.1016/j.jcp.2003.11.033

O. P. Le-maître, H. N. Najm, P. P. Pébay, R. G. Ghanem, and O. M. Knio, Multiresolution-analysis scheme for uncertainty quantication in chemical systems, SIAM J

M. Loève, Probability theory. I, Graduate Texts in Mathematics, vol.45, 1977.

M. Loève, Probability theory. II, Graduate Texts in Mathematics, vol.46, 1978.
DOI : 10.1007/978-1-4612-6257-2

G. Hermann and . Matthies, Stochastic nite elements: computational approaches to stochastic partial dierential equations, ZAMM Z. Angew. Math. Mech, vol.88, issue.11, p.849873, 2008.

G. Hermann, C. Matthies, and . Bucher, Finite elements for stochastic media problems, Comput. Methods Appl. Mech. Engrg, vol.168, pp.1-4317, 1999.

F. Nobile, R. Tempone, and C. G. Webster, An anisotropic sparse grid stochastic collocation method for partial dierential equations with random input data, SIAM J. Numer. Anal, vol.46, issue.5, p.24112442, 2008.

F. Nobile, R. Tempone, and C. G. Webster, A sparse grid stochastic collocation method for partial dierential equations with random input data, SIAM J. Numer. Anal, vol.46, issue.5, p.23092345, 2008.

F. Riesz, B. Sz, and . Nagy, Functional analysis. Dover Books on Advanced Mathematics Translated from the second French edition by, 1990.

J. V. Uspensky, On the convergence of quadrature formulas related to an innite interval, Trans. Amer. Math. Soc, vol.30, issue.3, p.542559, 1928.

T. Von, P. , and C. Schwab, Sparse nite element methods for operator equations with stochastic data, Appl. Math, vol.51, issue.2, p.145180, 2006.

X. Wan and G. E. Karniadakis, Solving elliptic problems with non- Gaussian spatially-dependent random coecients, Comput. Methods Appl. Mech. Engrg, vol.198, pp.21-26, 2009.

D. Xiu and J. S. Hesthaven, High-order collocation methods for dierential equations with random inputs, SIAM J. Sci. Comput, vol.27, issue.3, p.11181139, 2005.

D. Xiu and G. E. Karniadakis, The Wiener-Askey polynomial chaos for stochastic dierential equations, SIAM J. Sci. Comput, vol.24, issue.2, p.619644, 2002.

D. Zhang and Z. Lu, An ecient, high-order perturbation approach for ow in random porous media via karhunen-loève and polynomial expansions, J. Comput . Phys, vol.194, issue.2, p.773794, 2004.