R. J. Adler, The Geometry of Random Fields, 1981.
DOI : 10.1137/1.9780898718980

A. Ammar, B. Mokdad, F. Chinesta, and R. Keunings, A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids, Journal of Non-Newtonian Fluid Mechanics, vol.139, issue.3, pp.153-176, 2006.
DOI : 10.1016/j.jnnfm.2006.07.007

URL : https://hal.archives-ouvertes.fr/hal-01004909

A. Ammar, B. Mokdad, F. Chinesta, and R. Keunings, A new family of solvers for some classes of multidimensional partial dierential equations encountered in kinetic theory modelling of complex uids part II: Transient simulation using space-time separated representations, Journal of Non-Newtonian Fluid Mechanics, issue.23, p.14498121, 2007.

K. E. Atkinson, The Numerical Solution of Integral Equations of the Second Kind, 1997.

I. Babu?ka and P. Chatzipantelidis, On solving elliptic stochastic partial dierential equations, Computer Methods in Applied Mechanics and Engineering, vol.191, p.40934122, 2002.

I. Babu?ka and J. Chleboun, Eects of uncertainties in the domain on the solution of neumann boundary value problems in two spatial dimensions, Mathematics of Computation, issue.240, p.7113391370, 2002.

I. Babu?ka, K. Liu, and R. Tempone, Solving stochastic partial dierential equations based on the experimental data, TICAM Report, pp.2-18, 2002.

I. Babu?ka, F. Nobile, and R. Tempone, A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data, SIAM Journal on Numerical Analysis, vol.45, issue.3, pp.1005-1034, 2007.
DOI : 10.1137/050645142

I. Babu?ka, R. Tempone, and G. E. Zouraris, Solving elliptic boundary value problems with uncertain coecients by the nite element method: the stochastic formulation, Computer Methods in Applied Mechanics and Engineering, vol.194, p.12511294, 2005.

I. Babu?ka, R. Tempone, and G. E. Zouraris, Galerkin nite element approximations of stochastic elliptic dierential equations, TICAM Report, pp.2-38, 2002.

M. Barrault, Y. Maday, N. C. Nguyen, and A. T. Patera, An ???empirical interpolation??? method: application to efficient reduced-basis discretization of partial differential equations, Comptes Rendus Mathematique, vol.339, issue.9, p.667672, 2002.
DOI : 10.1016/j.crma.2004.08.006

URL : https://hal.archives-ouvertes.fr/hal-00021702

F. E. Benth and J. Gjerde, Convergence rates for nite element approximations of stochastic partial dierential equations, Stochastics and Stochastics Rep, vol.63, pp.3-4313326, 1998.

A. Berlinet and C. Thomas-agnan, Reproducing Kernel Hilbert Spaces in Probability and Statistics, 2004.
DOI : 10.1007/978-1-4419-9096-9

M. Berveiller, Stochastic nite elements: intrusive and non-intrusive methods for reliability analysis, 2005.

M. Berveiller, B. Sudret, and M. Lemaire, Stochastic nite element: a non intrusive approach by regression, European Journal of Computational Mechanics, vol.15, p.8192, 2006.

P. Besold, Solutions to Stochastic Partial Dierential Equations as Elements of Tensor Product Spaces, 2000.

G. Blatman and B. Sudret, Sparse polynomial chaos expansions and adaptive stochastic nite elements using a regression approach, Comptes Rendus Mécanique, vol.336, issue.6, p.518523, 2007.

G. Blatman, B. Sudret, and M. Berveiller, Quasi random numbers in stochastic nite element analysis, Mécanique & Industries, vol.8, p.289297, 2007.

H. Brézis, Analyse fonctionnelle : théorie et applications, 1983.

L. Bris, T. Lelievre, and Y. Maday, Results and questions on a nonlinear approximation approach for solving high-dimensional partial dierential equations, e-print, 2008.

H. Bungartz and M. Griebel, Sparse grids, Acta. Numer, vol.13, p.147269, 2004.

R. E. Caisch, Monte carlo and quasi-monte carlo methods, Acta. Numer, vol.7, p.149, 1998.

R. H. Cameron and W. T. Martin, The Orthogonal Development of Non-Linear Functionals in Series of Fourier-Hermite Functionals, The Annals of Mathematics, vol.48, issue.2, p.385392, 1947.
DOI : 10.2307/1969178

C. Canuto, M. Y. Hussaini, A. Quateroni, and T. A. Zang, Spectral methods in uid dynamics, 1988.

C. Canuto and T. Kozubek, A ctitious domain approach to the numerical solution of pdes in stochastic domains, Numerische Mathematik, vol.107, issue.2, p.257293, 2007.

Y. Cao, On Convergence rate of Wiener-Ito expansion for generalized random variables, Stochastics An International Journal of Probability and Stochastic Processes, vol.82, issue.3, p.179187, 2006.
DOI : 10.1137/040605278

F. Chinesta, A. Ammar, F. Lemarchand, P. Beauchene, and F. Boust, Alleviating mesh constraints: Model reduction, parallel time integration and high resolution homogenization, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.5, p.400413, 2008.
DOI : 10.1016/j.cma.2007.07.022

URL : https://hal.archives-ouvertes.fr/hal-01004980

S. Choi, R. V. Grandhi, and R. A. Caneld, Structural reliability under non-Gaussian stochastic behavior, Computers & Structures, vol.82, issue.13-14, p.11131121, 2004.
DOI : 10.1016/j.compstruc.2004.03.015

S. Choi, R. V. Grandhi, R. A. Caneld, and C. L. Pettit, Polynomial Chaos Expansion with Latin Hypercube Sampling for Estimating Response Variability, AIAA Journal, vol.42, issue.6, pp.1191-1198, 2004.
DOI : 10.2514/1.2220

G. Christakos, Random Field Models in Earth Sciences, 1992.

P. G. Ciarlet, The Finite Element Method for Elliptic Problems, 1978.

R. Courant and D. Hilbert, Methods of Mathematical Physics, 1989.

R. Dautray and J. Lions, Mathematical Analysis and Numerical Methods for Spectral theory and applications, Science and Technology, vol.3, 1990.

M. Deb, I. Babu?ka, and J. T. Oden, Solution of stochastic partial dierential equations using galerkin nite element techniques, Computer Methods in Applied Mechanics and Engineering, vol.190, p.63596372, 2001.

J. E. Dennis and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, SIAM, 1996.
DOI : 10.1137/1.9781611971200

O. Ditlevsen and H. Madsen, Strutural Reliability Methods, J. Wiley and Sons, 1996.

J. L. Doob, Stochastic Processes, 1953.

A. Doostan, R. Ghanem, and J. Red-horse, Stochastic model reduction for chaos representations, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.37-40, pp.37-403951, 2007.
DOI : 10.1016/j.cma.2006.10.047

C. G. Webster, F. Nobile, and R. Tempone, A sparse grid stochastic collocation method for partial dierential equations with random input data, SIAM Journal on Numerical Analysis, vol.46, issue.5, p.23092345, 2007.

P. Frauenfelder, C. Schwab, and R. A. Todor, Finite elements for elliptic problems with stochastic coecients, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.2 5, p.205228, 2005.

I. M. Gel-'fand and N. Y. Vilenkin, Applications of harmonic analysis, Generalized Functions, vol.4, 1964.

T. Gerstner and M. Griebel, Numerical integration using sparse grids, Numer. Algorithms, vol.18, p.209232, 1998.

T. Gerstner and M. Griebel, Dimension?Adaptive Tensor?Product Quadrature, Computing, vol.71, issue.1, p.6587, 2003.
DOI : 10.1007/s00607-003-0015-5

R. Ghanem, Ingredients for a general purpose stochastic nite elements implementation, Computer Methods in Applied Mechanics and Engineering, vol.168, 1934.

R. Ghanem, Stochastic nite elements for heterogeneous media with multiple random non-gaussian properties, ASCE J. Engrg. Mech, vol.125, p.2440, 1999.

R. Ghanem and R. M. Kruger, Numerical solution of spectral stochastic nite element systems, Computer Methods in Applied Mechanics and Engineering, vol.129, p.289303, 1996.

R. Ghanem, G. Saad, and A. Doostan, Ecient solution of stochastic systems: application to the embankment dam problem, Structural Safety, vol.29, issue.3, p.238251, 2007.

R. Ghanem and P. Spanos, Stochastic nite elements: a spectral approach, 1991.

D. Ghiocel and R. Ghanem, Stochastic nite-element analysis of seismic soil-structure interaction, ASCE Journal Engrg. Mech, vol.128, issue.1, p.6677, 2002.

P. Gosselet and C. Rey, On a selective reuse of Krylov subspaces in Newton-Krylov approaches for nonlinear elasticity, Domain decomposition methods in science and engineering, p.419426, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00277780

M. Grigoriu, Applied non-Gaussian Processes, 1995.

M. Grigoriu, Stochastic Calculus -Applications in Science and Engineering, 2002.

M. A. Gutiérrez and S. Krenk, Stochastic nite element methods, Encyclopedia of Computational Mechanics, p.657681, 2006.

S. Janson, Gaussian Hilbert Spaces, 1997.
DOI : 10.1017/CBO9780511526169

K. Karhunen, Zur spektraltheorie stochastischer prozesse, Ann. Acad. Sci. Fenn, vol.34, 1946.

A. Keese, Numerical Solution of Systems with Stochastic Uncertainties -A General Purpose Framework for Stochastic Finite Elements, 2003.

A. Keese, A review of recent developments in the numerical solution of stochastic pdes (stochastic nite elements, 2003.

A. Keese and H. G. Mathhies, Numerical methods and Smolyak quadrature for nonlinear stochastic partial dierential equations, SIAM J. Sci. Comput, vol.83, 2003.

A. Keese and H. G. Mathhies, Adaptivity and sensitivity for stochastic problems, Computational Stochastic Mechanics, p.311316, 2004.

A. Keese and H. G. Mathhies, Hierarchical parallelisation for the solution of stochastic nite element equations, Computer Methods in Applied Mechanics and Engineering, vol.83, p.10331047, 2005.

A. Khuri and J. Cornell, Response Surfaces: Designs and Analyses, 1987.

M. Kleiber and T. D. Hien, The Stochastic Finite Element Method. Basic Perturbation Technique and Computer Implementation, 1992.

P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Dierential Equations, 1995.

P. Ladevèze, Nonlinear Computational Structural Mechanics -New Approaches and Non-Incremental Methods of Calculation, 1999.

P. Ladevèze and E. Florentin, Verication of stochastic models in uncertain environments using the constitutive relation error method, Computer Methods in Applied Mechanics and Engineering, vol.196, pp.1-3225234, 2006.

P. Ladevèze and A. Nouy, On a multiscale computational strategy with time and space homogenization for structural mechanics, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.28-30, p.30613087, 2003.
DOI : 10.1016/S0045-7825(03)00341-4

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, R. G. Ghanem, and O. M. Knio, Multi-resolution analysis of Wiener-type uncertainty propagation schemes, Journal of Computational Physics, vol.197, issue.2, p.502531, 2004.
DOI : 10.1016/j.jcp.2003.12.020

O. P. Le-maître, O. M. Knio, H. N. Najm, and R. Ghanem, A stochastic projection method for uid ow. i. basic formulation, J. Comput. Physics, vol.173, p.481511, 2001.

O. P. Le-maître, M. T. Reagan, H. N. Najm, R. G. Ghanem, and O. M. Knio, A stochastic projection method for uid ow. ii. random process, J. Comput. Physics, vol.181, p.944, 2002.

A. Levy and J. Rubinstein, Some properties of smoothed principal component analysis for functional data, Journal of The Optical Society of America, vol.16, issue.1, p.2835, 1999.

M. Loève, Fonctions aléatoires du second ordre, CR Acad. Sci. Paris, vol.220, 1945.

M. Loève, Probability Theory. I, fourth edition, Graduate Texts in Mathematics, vol.45, 1977.

M. Loève, Probability Theory. II, fourth edition, Graduate Texts in Mathematics, vol.46, 1978.

L. Machiels, Y. Maday, and A. T. Patera, Output bounds for reduced-order approximations of elliptic partial dierential equations, Computer Methods in Applied Mechanics and Engineering, vol.190, pp.26-2734133426, 2001.

Y. Maday, A. T. Patera, and G. Turinici, Global a priori convergence theory for reducedbasis approximation of single-parameter symmetric coercive elliptic partial dierential equations, Comptes Rendus Mathematique, vol.335, issue.3, p.289294, 2002.

L. Mathelin and O. L. Maître, Dual-based a posteriori error estimate for stochastic nite element methods, Communications in Applied Mathematics and Computational Science, vol.2, p.83116, 2007.

H. G. Matthies, Uncertainty quantication with stochastic nite elements, Encyclopedia of Computational Mechanics, 2007.

H. G. Matthies, C. E. Brenner, C. G. Bucher, and C. G. Soares, Uncertainties in probabilistic numerical analysis of structures and solids -stochastic nite elements, Structural Safety, vol.19, issue.3, p.283336, 1997.

H. G. Matthies and A. Keese, Galerkin methods for linear and nonlinear elliptic stochastic partial dierential equations, Computer Methods in Applied Mechanics and Engineering, vol.194, pp.12-1612951331, 2005.

R. Melchers, Structural reliability analysis and prediction, 1999.

P. B. Nair, On the theoretical foundations of stochastic reduced basis methods, 19th AIAA Applied Aerodynamics Conference, 1677.
DOI : 10.2514/6.2001-1677

P. B. Nair and A. J. Keane, Stochastic Reduced Basis Methods, AIAA Journal, vol.40, issue.8, pp.1653-1664, 2002.
DOI : 10.2514/2.1837

H. Niederreiter, Random Number Generation and quasi-Monte Carlo Methods, SIAM, 1992.
DOI : 10.1137/1.9781611970081

A. Nouy, A generalized spectral decomposition technique to solve a class of linear stochastic partial dierential equations, Computer Methods in Applied Mechanics and Engineering, vol.196, pp.45-4845214537, 2007.

A. Nouy, M??thode de construction de bases spectrales g??n??ralis??es pour l'approximation de probl??mes stochastiques, M??canique & Industries, vol.8, issue.3, p.283288, 2007.
DOI : 10.1051/meca:2007050

A. Nouy, Generalized spectral decomposition method for solving stochastic nite element equations: invariant subspace problem and dedicated algorithms, Computer Methods in Applied Mechanics and Engineering, vol.197, p.47184736, 2008.
DOI : 10.1016/j.cma.2008.06.012

URL : https://hal.archives-ouvertes.fr/hal-00366613/file/AN_GSD_2008_preprint.pdf

A. Nouy, A. Clément, F. Schoefs, and N. Moës, An extended stochastic nite element method for solving stochastic partial dierential equations on random domains, Computer Methods in Applied Mechanics and Engineering, vol.197, p.46634682, 2008.

A. Nouy and P. Ladevèze, Multiscale Computational Strategy With Time and Space Homogenization: A Radial-Type Approximation Technique for Solving Microproblems, International Journal for Multiscale Computational Engineering, vol.2, issue.4, p.557574, 2004.
DOI : 10.1615/IntJMultCompEng.v2.i4.40

URL : https://hal.archives-ouvertes.fr/hal-00368058

A. Nouy and O. L. Maître, Generalized spectral decomposition method for stochastic non linear problems, Journal of Computational Physics, vol.228, issue.1, p.202235, 2009.

A. Nouy, F. Schoefs, and N. Moës, X-SFEM, a computational technique based on X-FEM to deal with random shapes, Revue europ??enne de m??canique num??rique, vol.16, issue.2, pp.277-293, 2007.
DOI : 10.3166/remn.16.277-293

URL : https://hal.archives-ouvertes.fr/hal-00368060

E. Novak and K. Ritter, Simple Cubature Formulas with High Polynomial Exactness, Constructive Approximation, vol.15, issue.4, p.499522, 1999.
DOI : 10.1007/s003659900119

M. F. Pellissetti and R. G. Ghanem, Iterative solution of systems of linear equations arising in the context of stochastic nite elements Advances in Engineering Software, p.607616, 2000.

K. Petras, Smolyak cubature of given polynomial degree with few nodes for increasing dimension, Numerische Mathematik, vol.93, issue.4, p.729753, 2003.
DOI : 10.1007/s002110200401

C. E. Powell and H. C. Elman, Block-diagonal precondioning for the spectral stochastic nite elements systems, 2007.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C -The Art of Scientic Computing, 1997.

B. Puig, F. Poirion, and C. Soize, Non-Gaussian simulation using Hermite polynomial expansion: convergences and algorithms, Probabilistic Engineering Mechanics, vol.17, issue.3, p.253264, 2002.
DOI : 10.1016/S0266-8920(02)00010-3

URL : https://hal.archives-ouvertes.fr/hal-00686282

M. T. Reagan, H. N. Najm, R. G. Ghanem, and O. M. Knio, Uncertainty quantication in reacting ow simulations through non-intrusive spectral projection, Combustion and Flames, vol.132, p.545555, 2003.

F. Riesz, B. Sz, and . Nagy, Functional Analysis, 1990.

F. Risler and C. Rey, Iterative accelerating algorithms with krylov subspaces for the solution to large-scale nonlinear problems, Numerical Algorithms, vol.23, p.130, 2000.

Y. A. Rozanov, Random Fields and Stochastic Partial Dierential Equations, 1998.
DOI : 10.1007/978-94-017-2838-6

URL : http://dx.doi.org/10.1016/s0898-1221(99)90199-2

Y. Maday, N. C. Nguyen, A. T. Patera, S. Boyaval, and C. L. Bris, A reduced basis approach for variational problems with stochastic parameters: Application to heat conduction with variable robin coecient, 2008.

Y. Saad, Numerical methods for large eigenvalue problems, 1992.
DOI : 10.1137/1.9781611970739

Y. Saad, Analysis of Augmented Krylov Subspace Methods, SIAM Journal on Matrix Analysis and Applications, vol.18, issue.2, p.435449, 1997.
DOI : 10.1137/S0895479895294289

Y. Saad, Iterative methods for sparse linear systems, 2000.
DOI : 10.1137/1.9780898718003

S. K. Sachdeva, P. B. Nair, and A. J. Keane, Comparative study of projection schemes for stochastic nite element analysis, Computer Methods in Applied Mechanics and Engineering, vol.195, pp.19-2223712392, 2006.

S. K. Sachdeva, P. B. Nair, and A. J. Keane, Hybridization of stochastic reduced basis methods with polynomial chaos expansions, Probabilistic Engineering Mechanics, vol.21, issue.2, p.182192, 2006.
DOI : 10.1016/j.probengmech.2005.09.003

A. Sameh and Z. Tong, The trace minimization method for the symmetric generalized eigenvalue problem, Journal of Computational and Applied Mathematics, vol.123, issue.1-2, p.155175, 2000.
DOI : 10.1016/S0377-0427(00)00391-5

G. I. Schüeller, A state-of-the-art report on computational stochastic mechanics, Probabilistic Engineering Mechanics, vol.12, issue.4, 1997.
DOI : 10.1016/S0266-8920(97)00003-9

M. Shinozuka and G. Deodatis, Simulation of stochastic processes and elds, Prob. Engrg. Mech, vol.14, p.203207, 1997.

S. A. Smolyak, Quadrature and interpolation formulas for tensor products of certain classes of functions, Sov. Math. Dokl, vol.3, p.240243, 1963.

I. M. Sobol, On quasi-Monte Carlo integrations, Mathematics and Computers in Simulation, vol.47, issue.2-5, p.103112, 1998.
DOI : 10.1016/S0378-4754(98)00096-2

C. Soize, Non-gaussian positive-denite matrix-valued random elds for elliptic stochastic partial dierential operators, Computer Methods in Applied Mechanics and Engineering, vol.195, pp.1-32664, 2006.

C. Soize and R. Ghanem, Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure, SIAM Journal on Scientific Computing, vol.26, issue.2, p.395410, 2004.
DOI : 10.1137/S1064827503424505

URL : https://hal.archives-ouvertes.fr/hal-00686211

G. Stefanou, A. Nouy, and A. Clément, Identication of random shapes from images through polynomial chaos expansion of random level-set functions, Int. J. for Numerical Methods in Engineering, 2009.

G. Strang and G. J. Fix, An Analysis of the Finite-Element Method, Journal of Applied Mechanics, vol.41, issue.1, 1986.
DOI : 10.1115/1.3423272

B. Sudret, Global sensitivity analysis using polynomial chaos expansions, Reliability Engineering & System Safety, vol.93, issue.7, p.964979, 2008.
DOI : 10.1016/j.ress.2007.04.002

URL : https://hal.archives-ouvertes.fr/hal-01432217

B. Sudret and A. Der-kiureghian, Stochastic nite element methods and reliability. a state-of-the-art report, 2000.

E. Vanmarcke, Random Fields: Analysis & Synthesis, Journal of Vibration Acoustics Stress and Reliability in Design, vol.107, issue.2, 1988.
DOI : 10.1115/1.3269255

J. B. Walsh, An introduction to stochastic partial dierential equations, Ecole d’été de Probabilités de Saint Flour XIV, 1984.

X. Wan and G. E. Karniadakis, An adaptive multi-element generalized polynomial chaos method for stochastic diential equations, J. Comp. Phys, vol.209, p.617642, 2005.

X. Wan and G. E. Karniadakis, Multi-element generalized polynomial chaos for arbitrary propability measures, SIAM J. Sci. Comp, vol.28, issue.3, p.901928, 2006.

N. Wiener, The Homogeneous Chaos, American Journal of Mathematics, vol.60, issue.4, p.897936, 1938.
DOI : 10.2307/2371268

K. Willcox and J. Peraire, Balanced model reduction via the proper orthogonal decomposition, AIAA Journal, vol.40, issue.11, p.23232330, 2002.

D. B. 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.