J. Bäck, F. Nobile, L. Tamellini, and R. Tempone, Stochastic Spectral Galerkin and Collocation Methods for PDEs with Random Coefficients: A Numerical Comparison, Spectral and High Order Methods for Partial Differential Equations, pp.43-62
DOI : 10.1007/978-3-642-15337-2_3

. Springer, Selected papers from the ICOSAHOM '09 conference, 2011.

J. Ballani and L. Grasedyck, A projection method to solve linear systems in tensor format. Numerical Linear Algebra with Applications, 2012.

J. Beck, F. Nobile, L. Tamellini, and R. Tempone, ON THE OPTIMAL POLYNOMIAL APPROXIMATION OF STOCHASTIC PDES BY GALERKIN AND COLLOCATION METHODS, Mathematical Models and Methods in Applied Sciences, vol.22, issue.09, 2011.
DOI : 10.1142/S0218202512500236

P. Binev, A. Cohen, W. Dahmen, R. Devore, G. Petrova et al., Convergence Rates for Greedy Algorithms in Reduced Basis Methods, SIAM Journal on Mathematical Analysis, vol.43, issue.3, pp.1457-1472, 2011.
DOI : 10.1137/100795772
URL : https://hal.archives-ouvertes.fr/hal-00767082

A. Buffa, Y. Maday, A. Patera, C. Prud?homme, and G. Turinici, convergence of the Greedy algorithm for the parametrized reduced basis method, ESAIM: Mathematical Modelling and Numerical Analysis, vol.46, issue.3, pp.595-603, 2012.
DOI : 10.1051/m2an/2011056
URL : https://hal.archives-ouvertes.fr/hal-00659314

E. Cances, V. Ehrlacher, and T. Lelievre, CONVERGENCE OF A GREEDY ALGORITHM FOR HIGH-DIMENSIONAL CONVEX NONLINEAR PROBLEMS, Mathematical Models and Methods in Applied Sciences, vol.21, issue.12, pp.2433-2467, 2011.
DOI : 10.1142/S0218202511005799
URL : https://hal.archives-ouvertes.fr/hal-00469622

C. Canuto, M. Y. Hussaini, A. Quateroni, and T. A. Zang, Spectral methods in fluid dynamics, 1988.
DOI : 10.1007/978-3-642-84108-8

M. Chevreuil and A. Nouy, Model order reduction based on proper generalized decomposition for the propagation of uncertainties in structural dynamics, International Journal for Numerical Methods in Engineering, vol.5, issue.2-4, pp.241-268, 2012.
DOI : 10.1002/nme.3249
URL : https://hal.archives-ouvertes.fr/hal-00603342

F. Chinesta, P. Ladeveze, and E. Cueto, A Short Review on Model Order Reduction Based on Proper Generalized Decomposition, Archives of Computational Methods in Engineering, vol.69, issue.9, pp.395-404, 2011.
DOI : 10.1007/s11831-011-9064-7
URL : https://hal.archives-ouvertes.fr/hal-01004940

A. Cohen, R. Devore, and C. Schwab, Analytic regularity and polynomial approximation of parametric and stochastic elliptic PDEs, 2010.

A. Cohen, R. Devore, and C. Schwab, Convergence Rates of Best N-term Galerkin Approximations for a Class of Elliptic sPDEs, Foundations of Computational Mathematics, vol.60, issue.6, pp.615-646, 1007.
DOI : 10.1007/s10208-010-9072-2

A. Doostan and G. Iaccarino, A least-squares approximation of partial differential equations with high-dimensional random inputs, Journal of Computational Physics, vol.228, issue.12, pp.4332-4345, 2009.
DOI : 10.1016/j.jcp.2009.03.006

A. Falco and A. Nouy, A Proper Generalized Decomposition for the solution of elliptic problems in abstract form by using a functional Eckart???Young approach, Journal of Mathematical Analysis and Applications, vol.376, issue.2, pp.469-480, 2011.
DOI : 10.1016/j.jmaa.2010.12.003
URL : https://hal.archives-ouvertes.fr/hal-00461094

A. Falco and A. Nouy, Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces, Numerische Mathematik, vol.115, issue.45???48, 2012.
DOI : 10.1007/s00211-011-0437-5
URL : https://hal.archives-ouvertes.fr/hal-00609108

R. G. Ghanem and P. D. Spanos, Stochastic Finite Elements: A Spectral Approach, 2002.
DOI : 10.1007/978-1-4612-3094-6

N. Boris, C. Khoromsk?, and . Schwab, Tensor-structured galerkin approximation of parametric and stochastic elliptic pdes, SIAM Journal on Scientific Computing, vol.33, issue.1, pp.364-385, 2011.

O. M. Knio and O. P. Le-ma??trema??tre, Uncertainty propagation in CFD using polynomial chaos decomposition, Fluid Dynamics Research, vol.38, issue.9, pp.616-640, 2006.
DOI : 10.1016/j.fluiddyn.2005.12.003

O. , L. Ma??trema??tre, M. T. Reagan, B. Debusschere, H. N. Najm et al., Natural convection in a closed cavity under stochastic, non-Boussinesq conditions, J. Sci. Comput, vol.26, issue.2, pp.375-394, 2004.

O. P. Le-ma??trema??tre and O. M. Knio, Spectral methods for uncertainty quantification. Scientific Computation, 2010.

O. P. Le-ma??trema??tre, O. M. Knio, H. N. Najm, and R. G. Ghanem, A Stochastic Projection Method for Fluid Flow, Journal of Computational Physics, vol.173, issue.2, pp.481-511, 2001.
DOI : 10.1006/jcph.2001.6889

O. P. Le-ma??trema??tre, M. T. Reagan, H. N. Najm, R. G. Ghanem, and O. M. Knio, A Stochastic Projection Method for Fluid Flow, Journal of Computational Physics, vol.181, issue.1, pp.9-44, 2002.
DOI : 10.1006/jcph.2002.7104

Y. Maday, A. T. Patera, and G. Turinici, Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations, Comptes Rendus Mathematique, vol.335, issue.3, pp.289-294, 2002.
DOI : 10.1016/S1631-073X(02)02466-4
URL : https://hal.archives-ouvertes.fr/hal-00798389

O. and L. Ma??trema??tre, A Newton method for the resolution of steady stochastic Navier-Stokes equations. Computers and Fluids, 2007.

H. G. Matthies and E. Zander, Solving stochastic systems with low-rank tensor compression, Linear Algebra and its Applications, vol.436, issue.10, 2012.
DOI : 10.1016/j.laa.2011.04.017

H. N. Najm, Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics, Annual Review of Fluid Mechanics, vol.41, issue.1, pp.35-52, 2009.
DOI : 10.1146/annurev.fluid.010908.165248

A. Nouy, A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.45-48, pp.45-484521, 2007.
DOI : 10.1016/j.cma.2007.05.016
URL : https://hal.archives-ouvertes.fr/hal-00366619

A. Nouy, Generalized spectral decomposition method for solving stochastic finite element equations: Invariant subspace problem and dedicated algorithms, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.51-52, pp.4718-4736, 2008.
DOI : 10.1016/j.cma.2008.06.012
URL : https://hal.archives-ouvertes.fr/hal-00366613

A. Nouy, Recent Developments in Spectral Stochastic Methods for??the??Numerical Solution of Stochastic Partial Differential Equations, Archives of Computational Methods in Engineering, vol.24, issue.2, pp.251-285, 2009.
DOI : 10.1007/s11831-009-9034-5
URL : https://hal.archives-ouvertes.fr/hal-00366636

A. Nouy, A priori model reduction through Proper Generalized Decomposition for solving time-dependent partial differential equations, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.23-24, pp.23-241603, 2010.
DOI : 10.1016/j.cma.2010.01.009
URL : https://hal.archives-ouvertes.fr/hal-00455635

A. Nouy, Proper Generalized Decompositions and Separated Representations for the Numerical Solution of High Dimensional Stochastic Problems, Archives of Computational Methods in Engineering, vol.225, issue.1, pp.403-434, 2010.
DOI : 10.1007/s11831-010-9054-1
URL : https://hal.archives-ouvertes.fr/hal-00461099

A. Nouy and O. P. Le-ma??trema??tre, Generalized spectral decomposition for stochastic nonlinear problems, Journal of Computational Physics, vol.228, issue.1, pp.202-235, 2009.
DOI : 10.1016/j.jcp.2008.09.010

C. Prud-'homme, D. Rovas, K. Veroy, Y. Maday, A. T. Patera et al., Reliable real-time solution of parametrized partial differential equations: Reduced-basis output bound methods, Journal of Fluids Engineering, vol.124, issue.1, pp.70-80, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00798326

A. Quarteroni and G. Rozza, Numerical solution of parametrized Navier???Stokes equations by reduced basis methods, Numerical Methods for Partial Differential Equations, vol.47, issue.4, pp.923-948, 2007.
DOI : 10.1002/num.20249

G. Rozza, D. B. Huynh, and A. T. Patera, Reduced Basis Approximation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations, Archives of Computational Methods in Engineering, vol.40, issue.11, pp.229-275, 2008.
DOI : 10.1007/s11831-008-9019-9

K. Veroy, C. Prud-'homme, and A. T. Patera, Reduced-basis approximation of the viscous Burgers equation: rigorous a posteriori error bounds, Comptes Rendus Mathematique, vol.337, issue.9, pp.619-624, 2003.
DOI : 10.1016/j.crma.2003.09.023
URL : https://hal.archives-ouvertes.fr/hal-01219048

D. B. Xiu and G. E. Karniadakis, The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations, SIAM Journal on Scientific Computing, vol.24, issue.2, pp.619-644, 2002.
DOI : 10.1137/S1064827501387826

D. B. Xiu and G. E. Karniadakis, Modeling uncertainty in flow simulations via generalized polynomial chaos, Journal of Computational Physics, vol.187, issue.1, pp.137-167, 2003.
DOI : 10.1016/S0021-9991(03)00092-5