H. G. Matthies, Stochastic finite elements: Computational approaches to stochastic partial differential equations, ZAMM, vol.196, issue.11, pp.849-873, 2008.
DOI : 10.1002/zamm.200800095

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

D. Xiu, Fast numerical methods for stochastic computations: a review, Communication in Computational Physics, vol.5, issue.2-4, pp.242-272, 2009.

O. P. Le-ma??trema??tre and O. M. Knio, Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics, 2010.
DOI : 10.1007/978-90-481-3520-2

A. Sarkar, N. Benabbou, and R. Ghanem, Domain decomposition of stochastic PDEs: Theoretical formulations, International Journal for Numerical Methods in Engineering, vol.31, issue.4, pp.689-701, 2009.
DOI : 10.1002/nme.2431

X. F. Xu, A multiscale stochastic finite element method on elliptic problems involving uncertainties, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.25-28, pp.2723-2736, 2007.
DOI : 10.1016/j.cma.2007.02.002

X. F. Xu, X. Chen, and L. Shen, A Green-function-based multiscale method for uncertainty quantification of finite body random heterogeneous materials, Computers & Structures, vol.87, issue.21-22, pp.1416-1426, 2009.
DOI : 10.1016/j.compstruc.2009.05.009

B. Ganapathysubramanian and N. Zabaras, A stochastic multiscale framework for modeling flow through random heterogeneous porous media, Journal of Computational Physics, vol.228, issue.2, pp.591-618, 2009.
DOI : 10.1016/j.jcp.2008.10.006

X. Ma and N. Zabaras, A stochastic mixed finite element heterogeneous multiscale method for flow in porous media, Journal of Computational Physics, vol.230, issue.12, pp.4696-4722, 2011.
DOI : 10.1016/j.jcp.2011.03.001

E. Stein and S. Ohnimus, Coupled model- and solution-adaptivity in the finite-element method, Computer Methods in Applied Mechanics and Engineering, vol.150, issue.1-4, pp.327-350, 1997.
DOI : 10.1016/S0045-7825(97)00082-0

A. Düster, A. Niggl, and E. Rank, Applying the hp???d version of the FEM to locally enhance dimensionally reduced models, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.37-40, pp.3524-3533, 2007.
DOI : 10.1016/j.cma.2006.10.018

J. M. Melenk and I. Babu?ka, The partition of unity method: basic theory and applications, Computer Methods in Applied Mechanics and Engineering, vol.39, pp.289-314, 1996.

N. Moës, J. Dolbow, and T. Belytschko, A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering, vol.46, issue.1, pp.131-150, 1999.
DOI : 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.3.CO;2-A

L. Gendre, O. Allix, P. Gosselet, and F. Comte, Non-intrusive and exact global/local techniques for structural problems with local plasticity, Computational Mechanics, vol.36, issue.1, pp.233-245, 2009.
DOI : 10.1007/s00466-009-0372-9

URL : https://hal.archives-ouvertes.fr/hal-00437023

L. Gendre, O. Allix, and P. Gosselet, A two-scale approximation of the Schur complement and its use for non-intrusive coupling, International Journal for Numerical Methods in Engineering, vol.64, issue.1-4, pp.889-905, 2011.
DOI : 10.1002/nme.3142

URL : https://hal.archives-ouvertes.fr/hal-01224373

A. Lozinski, Méthodes numériques et modélisation pour certainsprobì emes multi-´ echelles, 2010.

A. Lozinski and O. Pironneau, Numerical zoom for advection diffusion problems with localized multiscales, Numerical Methods for Partial Differential Equations, vol.38, issue.1, pp.197-207, 2011.
DOI : 10.1002/num.20642

URL : https://hal.archives-ouvertes.fr/hal-00631122

C. Hager, P. Hauret, P. L. Tallec, and B. I. Wohlmuth, Solving dynamic contact problems with local refinement in space and time, Computer Methods in Applied Mechanics and Engineering, vol.201, issue.204, pp.201-20425, 2012.
DOI : 10.1016/j.cma.2011.09.006

URL : https://hal.archives-ouvertes.fr/hal-01393141

F. Brezzi, J. Lions, and O. Pironneau, Analysis of a Chimera method, Comptes Rendus de l'Académie des Sciences -Series I -Mathematics, pp.655-660, 2001.
DOI : 10.1016/S0764-4442(01)01904-8

G. J. Wagner and W. K. Liu, Coupling of atomistic and continuum simulations using a bridging scale decomposition, Journal of Computational Physics, vol.190, issue.1, pp.249-274, 2003.
DOI : 10.1016/S0021-9991(03)00273-0

S. P. Xiao and T. Belytschko, A bridging domain method for coupling continua with molecular dynamics, Computer Methods in Applied Mechanics and Engineering, vol.193, issue.17-20, pp.17-201645, 2004.
DOI : 10.1016/j.cma.2003.12.053

H. and B. Dhia, Multiscale mechanical problems: the Arlequin method Comptes Rendus de l'Académie des Sciences, pp.899-904, 1998.

L. Chamoin, J. T. Oden, and S. Prudhomme, A stochastic coupling method for atomic-to-continuum Monte-Carlo simulations, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.43-44, pp.3530-3546, 2008.
DOI : 10.1016/j.cma.2008.04.013

R. Cottereau, D. Clouteau, H. B. Dhia, and C. Zaccardi, A stochastic-deterministic coupling method for continuum mechanics, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.47-48, pp.3280-3288, 2011.
DOI : 10.1016/j.cma.2011.07.010

URL : https://hal.archives-ouvertes.fr/hal-00709540

W. Hackbusch, Tensor Spaces and Numerical Tensor Calculus, of Series in Computational Mathematics, 2012.
DOI : 10.1007/978-3-642-28027-6

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

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

C. Canuto and T. Kozubek, A fictitious domain approach to the numerical solution of PDEs in stochastic domains, Numerische Mathematik, vol.28, issue.2, pp.257-293, 2007.
DOI : 10.1007/s00211-007-0086-x

A. Nouy, A. Clément, F. Schoefs, and N. Moës, An extended stochastic finite element method for solving stochastic partial differential equations on random domains, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.51-52, pp.51-524663, 2008.
DOI : 10.1016/j.cma.2008.06.010

URL : https://hal.archives-ouvertes.fr/hal-00366617

A. Nouy, M. Chevreuil, and E. Safatly, Fictitious domain method and separated representations for the solution of boundary value problems on uncertain parameterized domains, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.45-46, pp.3066-3082, 2011.
DOI : 10.1016/j.cma.2011.07.002

URL : https://hal.archives-ouvertes.fr/hal-00662564

B. I. Wohlmuth, Discretization methods and iterative solvers based on domain decomposition, 2001.
DOI : 10.1007/978-3-642-56767-4

D. Xiu and D. M. Tartakovsky, Numerical Methods for Differential Equations in Random Domains, SIAM Journal on Scientific Computing, vol.28, issue.3, pp.1167-1185, 2006.
DOI : 10.1137/040613160

U. Bnerjee, I. Babu?ka, and J. E. Osborn, Survey of meshless and generalized finite element methods: A unified approach, Acta Numerica, vol.12, pp.1-125, 2003.

J. Xu, Iterative Methods by Space Decomposition and Subspace Correction, SIAM Review, vol.34, issue.4, pp.581-613, 1992.
DOI : 10.1137/1034116

T. G. Kolda and B. W. Bader, Tensor Decompositions and Applications, SIAM Review, vol.51, issue.3, pp.455-500, 2009.
DOI : 10.1137/07070111X

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.130.782

F. Chinesta, P. Ladevèze, 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