I. Babu?ka, F. Nobile, and R. Tempone, A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data, In: SIAM Journal on Numerical Analysis, vol.453, pp.1005-1034, 2007.

I. Babu?ka, R. Tempone, and G. E. Zouraris, Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations, SIAM Journal on Numerical Analysis, vol.42, issue.2, pp.800-825, 2004.
DOI : 10.1137/S0036142902418680

G. Blatman and B. Sudret, An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis, Probabilistic Engineering Mechanics 25, pp.183-197, 2010.
DOI : 10.1016/j.probengmech.2009.10.003

G. Blatman and B. Sudret, Adaptive sparse polynomial chaos expansion based on least angle regression, Journal of Computational Physics, vol.230, issue.6, pp.2345-2367, 2011.
DOI : 10.1016/j.jcp.2010.12.021

G. C. Cawley and N. L. Talbot, Fast exact leave-one-out cross-validation of sparse least-squares support vector machines, Neural Networks 17.10, pp.1467-1475, 2004.
DOI : 10.1016/j.neunet.2004.07.002

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.103.9699

O. Chapelle, V. Vapnik, and Y. English, Model Selection for Small Sample Regression, Machine Learning, vol.48, pp.1-3, 2002.

M. Chevreuil, A. Nouy, and E. Safatly, A multiscale method with patch for the solution of stochastic partial differential equations with localized uncertainties, Computer Methods in Applied Mechanics and Engineering, vol.255, issue.0, pp.255-274, 2013.
DOI : 10.1016/j.cma.2012.12.003

URL : https://hal.archives-ouvertes.fr/hal-00733739

I. References, A. Chkifa, A. Cohen, and C. Schwab, High-Dimensional Adaptive Sparse Polynomial Interpolation and Applications to Parametric PDEs, English. In: Foundations of Computational Mathematics 14.4, pp.601-633, 2014.

A. Chkifa, Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs, ESAIM: Mathematical Modelling and Numerical Analysis, vol.47, issue.1, pp.253-280, 2013.
DOI : 10.1051/m2an/2012027

URL : http://e-collection.library.ethz.ch/eserv/eth:47530/eth-47530-01.pdf

M. K. Deb, I. M. Babu?ka, and J. Oden, Solution of stochastic partial differential equations using Galerkin finite element techniques, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.48, pp.6359-6372, 0190.
DOI : 10.1016/S0045-7825(01)00237-7

M. Duval, Non-intrusive Coupling: Recent Advances and Scalable Nonlinear Domain Decomposition, English. In: Archives of Computational Methods in Engineering, pp.1-22, 2014.
DOI : 10.1016/S0045-7825(96)01106-1

URL : https://hal.archives-ouvertes.fr/hal-01065538

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 : 10.1016/S0045-7949(96)00165-4

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

L. Gendre, 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

R. Ghanem, Stochastic Finite Elements with Multiple Random Non-Gaussian Properties, Journal of Engineering Mechanics, vol.125, issue.1, 1999.
DOI : 10.1061/(ASCE)0733-9399(1999)125:1(26)

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.15.3215

I. References, R. G. Ghanem, and P. D. Spanos, Stochastic Finite Elements: A Spectral Approach, 1991.

C. Hager, Solving dynamic contact problems with local refinement in space and time, Computer Methods in Applied Mechanics and Engineering, vol.201, issue.204, pp.25-41, 2012.
DOI : 10.1016/j.cma.2011.09.006

URL : https://hal.archives-ouvertes.fr/hal-00655514

B. M. Irons and R. C. Tuck, A version of the Aitken accelerator for computer iteration, International Journal for Numerical Methods in Engineering, vol.1, issue.3, pp.275-277, 1969.
DOI : 10.1002/nme.1620010306

U. Küttler and W. A. Wall, Fixed-point fluid???structure interaction solvers with dynamic relaxation, English. In: Computational Mechanics 43.1, pp.61-72, 2008.
DOI : 10.1007/s00466-008-0255-5

L. Maître and O. , Multi-resolution analysis of Wiener-type uncertainty propagation schemes, Journal of Computational Physics, vol.197, issue.2, pp.502-531, 2004.
DOI : 10.1016/j.jcp.2003.12.020

L. Maître and O. , Uncertainty propagation using Wiener???Haar expansions, Journal of Computational Physics, vol.197, issue.1, pp.28-57, 2004.
DOI : 10.1016/j.jcp.2003.11.033

Y. Liu, Q. Sun, and X. Fan, A non-intrusive global/local algorithm with non-matching interface: Derivation and numerical validation, Computer Methods in Applied Mechanics and Engineering, vol.277, issue.0, pp.81-103, 2014.
DOI : 10.1016/j.cma.2014.04.012

A. Lozinski, Méthodes numériques et modélisation pour certains problèmes multi-échelles " . Habilitation à diriger des recherches, 2010.

A. J. Macleod, Acceleration of vector sequences by multi-dimensional ??2 methods, Communications in Applied Numerical Methods 2.4, pp.385-392, 1986.
DOI : 10.1002/cnm.1630020409

I. References and A. Nouy, A priori model reduction through Proper Generalized Decomposition for solving time-dependent partial differential equations, In: Computer Methods in Applied Mechanics and Engineering, vol.199, pp.23-24, 2010.

A. Nouy and F. Pled, A multiscale method for semi-linear elliptic equations with localized uncertainties and non-linearities, p.2, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01507489

N. Parés, P. Díez, and A. Huerta, Bounds of functional outputs for parabolic problems. Part I: Exact bounds of the discontinuous Galerkin time discretization, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.19-20, pp.19-20, 2008.
DOI : 10.1016/j.cma.2007.08.025

S. Andrea, K. C. , and E. M. Scott, Sensitivity Analysis, 2000.

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, pp.395-410, 2004.
DOI : 10.1137/S1064827503424505

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

B. Sudret, Global sensitivity analysis using polynomial chaos expansions, Reliability Engineering & System Safety 93.7, pp.964-979, 2008.
DOI : 10.1016/j.ress.2007.04.002

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

X. Wan and G. E. Karniadakis, An adaptive multi-element generalized polynomial chaos method for stochastic differential equations, Journal of Computational Physics, vol.209, issue.2, pp.617-642, 2005.
DOI : 10.1016/j.jcp.2005.03.023

URL : http://www.dtic.mil/get-tr-doc/pdf?AD=ADA458984

J. Whitcomb, Iterative global/local finite element analysis, Computers & Structures, vol.40, issue.4, pp.1027-1031, 1991.
DOI : 10.1016/0045-7949(91)90334-I

D. Xiu and J. Hesthaven, High-Order Collocation Methods for Differential Equations with Random Inputs, SIAM Journal on Scientific Computing, vol.27, issue.3, pp.1118-1139, 2005.
DOI : 10.1137/040615201

URL : https://infoscience.epfl.ch/record/190489/files/SIAM J Sci Comput 2005 Xiu.pdf

V. References, D. Xiu, and G. Karniadakis, The Wiener?Askey Polynomial Chaos for Stochastic Differential Equations, In: SIAM Journal on Scientific Computing, vol.24, issue.2, pp.619-644, 2002.

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