M. Ainsworth and J. T. Oden, A posteriori error estimation in finite element analysis, Computer Methods in Applied Mechanics and Engineering, vol.142, issue.1-2, 2000.
DOI : 10.1016/S0045-7825(96)01107-3

A. Fernandes, V. Lopez-caballero, F. Costa-d-'aguiar, and S. , Probabilistic analysis of numerical simulated railway track global stiffness, Computers and Geotechnics, vol.55, pp.267-276, 2014.
DOI : 10.1016/j.compgeo.2013.09.017

URL : https://hal.archives-ouvertes.fr/hal-00869179

H. Askes and A. Rodriguez-ferran, A combined rh???adaptive scheme based on domain subdivision. Formulation and linear examples, International Journal for Numerical Methods in Engineering, vol.51, issue.3, pp.253-273, 2001.
DOI : 10.1002/nme.142

I. Babu?ka, F. Nobile, and R. Tempone, A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data, SIAM Review, vol.52, issue.2, pp.317-355, 2007.
DOI : 10.1137/100786356

I. Babu?ka and W. C. Rheinboldt, Error Estimates for Adaptive Finite Element Computations, SIAM Journal on Numerical Analysis, vol.15, issue.4, pp.736-755, 1978.
DOI : 10.1137/0715049

I. Babu?ka and W. C. Rheinboldt, A-posteriori error estimates for the finite element method, International Journal for Numerical Methods in Engineering, vol.15, issue.10, pp.1597-1615, 1978.
DOI : 10.1002/nme.1620121010

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

I. Babu?ka, J. Whiteman, and T. Strouboulis, Finite elements: an introduction to the method and error estimation, 2010.

I. Baydoun, E. Savin, R. Cottereau, D. Clouteau, and J. Guilleminot, Kinetic modeling of multiple scattering of elastic waves in heterogeneous anisotropic media, Wave Motion, vol.51, issue.8, 2014.
DOI : 10.1016/j.wavemoti.2014.08.001

URL : https://hal.archives-ouvertes.fr/hal-01083250

A. Bespalov, C. E. Powell, and D. Silvester, A Priori Error Analysis of Stochastic Galerkin Mixed Approximations of Elliptic PDEs with Random Data, SIAM Journal on Numerical Analysis, vol.50, issue.4, pp.2039-2063, 2012.
DOI : 10.1137/110854898

T. Butler, C. Dawson, and T. Wildey, A Posteriori Error Analysis of Stochastic Differential Equations Using Polynomial Chaos Expansions, SIAM Journal on Scientific Computing, vol.33, issue.3, pp.1267-1291, 2011.
DOI : 10.1137/100795760

R. E. Caflisch, Monte Carlo and quasi-Monte Carlo methods, Acta Numerica, vol.73, pp.1-49, 1998.
DOI : 10.1137/S0036142994277468

L. Chamoin, E. Florentin, S. Pavot, and V. Visseq, Robust goal-oriented error estimation based on the constitutive relation error for stochastic problems, Computers & Structures, vol.106, issue.107, pp.189-195, 2012.
DOI : 10.1016/j.compstruc.2012.05.002

URL : https://hal.archives-ouvertes.fr/hal-00776138

J. Charrier, Strong and Weak Error Estimates for Elliptic Partial Differential Equations with Random Coefficients, SIAM Journal on Numerical Analysis, vol.50, issue.1, pp.216-246, 2012.
DOI : 10.1137/100800531

URL : https://hal.archives-ouvertes.fr/inria-00490045

J. Charrier, R. Scheichl, and A. L. Teckentrup, Finite Element Error Analysis of Elliptic PDEs with Random Coefficients and Its Application to Multilevel Monte Carlo Methods, SIAM Journal on Numerical Analysis, vol.51, issue.1, pp.322-352, 1137.
DOI : 10.1137/110853054

M. Cho and S. Jun, r-Adaptive mesh generation for shell finite element analysis, Journal of Computational Physics, vol.199, issue.1, pp.291-316, 2004.
DOI : 10.1016/j.jcp.2004.02.007

S. K. Choi, R. V. Gandhi, and R. A. Canfield, Reliability-based structural design, 2006.

A. Chorin, Gaussian fields and random flow, Journal of Fluid Mechanics, vol.25, issue.01, pp.21-32, 1974.
DOI : 10.1063/1.1704327

D. Clouteau, R. Cottereau, and G. Lombaert, Dynamics of structures coupled with elastic media???A review of numerical models and methods, Journal of Sound and Vibration, vol.332, issue.10, pp.2415-2436, 2013.
DOI : 10.1016/j.jsv.2012.10.011

URL : https://hal.archives-ouvertes.fr/hal-00795002

R. Cottereau, Numerical strategy for unbiased homogenization of random materials, International Journal for Numerical Methods in Engineering, vol.19, issue.1-3, pp.71-90, 2013.
DOI : 10.1002/nme.4502

URL : https://hal.archives-ouvertes.fr/hal-00837633

R. Cottereau, D. Clouteau, and C. Soize, Probabilistic impedance of foundation: Impact of the seismic design on uncertain soils, Earthquake Engineering & Structural Dynamics, vol.197, issue.6, pp.899-918, 2007.
DOI : 10.1002/eqe.794

URL : https://hal.archives-ouvertes.fr/hal-00685116

M. K. Deb, I. Babu?ka, and J. T. 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, 2001.
DOI : 10.1016/S0045-7825(01)00237-7

B. Debusschere, H. N. Najm, A. Matta, O. Knio, R. Ghanem et al., Protein labeling reactions in electrochemical microchannel flow: Numerical simulation and uncertainty propagation, Physics of Fluids, vol.15, issue.8, pp.2238-2250, 2003.
DOI : 10.1063/1.1582857

Y. Efendiev and A. Pankov, Numerical Homogenization of Nonlinear Random Parabolic Operators, Multiscale Modeling & Simulation, vol.2, issue.2, pp.237-268, 2004.
DOI : 10.1137/030600266

E. Florentin and P. Díez, Adaptive reduced basis strategy based on goal oriented error assessment for stochastic problems, Computer Methods in Applied Mechanics and Engineering, vol.225, issue.228, pp.225-228, 2012.
DOI : 10.1016/j.cma.2012.03.016

J. Foo, X. Wan, and G. E. Karniadakis, The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications, Journal of Computational Physics, vol.227, issue.22, pp.9572-9595, 2008.
DOI : 10.1016/j.jcp.2008.07.009

A. Frankel and R. W. Clayton, A finite-difference simulation of wave propagation in twodimensional random media, Bull. Seismological. Soc. Amer, vol.74, issue.6, pp.2167-2186, 1984.

R. G. Ghanem and P. D. Spanos, Stochastic finite elements: a spectral approach, 1991.
DOI : 10.1007/978-1-4612-3094-6

M. Grajewski, M. Köster, and S. Turek, Numerical analysis and implementational aspects of a new multilevel grid deformation method, Applied Numerical Mathematics, vol.60, issue.8, pp.767-781, 2010.
DOI : 10.1016/j.apnum.2010.03.017

K. Holliger, -wave sonic logs, Geophysical Journal International, vol.125, issue.3, pp.813-829, 1996.
DOI : 10.1111/j.1365-246X.1996.tb06025.x

URL : https://hal.archives-ouvertes.fr/hal-00259588

A. Huerta, A. Rodriguez-ferran, P. Díez, and J. Sarrate, Adaptive finite element strategies based on error assessment, 10¡1803::AID-NME725¿3.0.CO, pp.1803-18181097, 1999.

L. Huyse and M. A. Maes, Random Field Modeling of Elastic Properties Using Homogenization, Journal of Engineering Mechanics, vol.127, issue.1, pp.27-360733, 2001.
DOI : 10.1061/(ASCE)0733-9399(2001)127:1(27)

P. Jehel and R. Cottereau, On damping created by heterogeneous yielding in the numerical analysis of nonlinear RC frame elements, Comp. & Struct, 2014.

P. Ladevèze and E. Florentin, Verification of stochastic models in uncertain environments using the constitutive relation error method, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.1-3, pp.225-234, 2006.
DOI : 10.1016/j.cma.2006.03.006

P. Ladevèze and J. P. Pelle, Mastering calculations in linear and nonlinear mechanics, Mechanical Engineering, 2005.

L. Bris and C. G. , Some Numerical Approaches for Weakly Random Homogenization, Numerical Mathematics and Advanced Applications, pp.29-45, 2009.
DOI : 10.1007/978-3-642-11795-4_3

L. Ma??trema??tre, O. P. Knio, and O. M. , Spectral methods for uncertainty quantification: with applications to computational fluid dynamics, 2010.

D. L. Littlefield, The use of r-adaptivity with local, intermittent remesh for modeling hypervelocity impact and penetration, International Journal of Impact Engineering, vol.26, issue.1-10, pp.1-10, 2001.
DOI : 10.1016/S0734-743X(01)00093-8

D. Materna and F. J. Barthold, Goal-oriented r-adaptivity based on variational arguments in the physical and material spaces, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.41-44, pp.41-44, 2009.
DOI : 10.1016/j.cma.2009.06.015

L. Mathelin and O. Le-ma??trema??tre, error estimate for stochastic finite element methods, Communications in Applied Mathematics and Computational Science, vol.2, issue.1, pp.83-115, 2007.
DOI : 10.2140/camcos.2007.2.83

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

J. T. Oden, I. Babu?ka, F. Nobile, Y. Feng, and R. Tempone, Theory and methodology for estimation and control of errors due to modeling, approximation, and uncertainty, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.2-5, pp.195-204, 2005.
DOI : 10.1016/j.cma.2003.06.003

M. Ostoja-starzewski, Microstructural randomness and scaling in mechanics of materials, 2007.
DOI : 10.1201/9781420010275

J. Peraire, M. Vahdati, K. Morgan, and O. C. Zienkiewicz, Adaptive remeshing for compressible flow computations, Journal of Computational Physics, vol.72, issue.2, pp.449-4660021, 1987.
DOI : 10.1016/0021-9991(87)90093-3

K. K. Phoon, Reliability-based design in geotechnical engineering, 2008.

M. D. Piggott, C. C. Pain, G. J. Gorman, P. W. Power, and A. J. Goddard, h, r, and hr adaptivity with applications in numerical ocean modelling, Ocean Modelling, vol.10, issue.1-2, pp.95-113, 2005.
DOI : 10.1016/j.ocemod.2004.07.007

R. Popescu, G. Deodatis, and A. Nobahar, Effects of random heterogeneity of soil properties on bearing capacity, Probabilistic Engineering Mechanics, vol.20, issue.4, pp.324-341, 2005.
DOI : 10.1016/j.probengmech.2005.06.003

A. Rajagopal and S. M. Sivakumar, A combined r-h adaptive strategy based on material forces and error assessment for plane problems and bimaterial interfaces, Computational Mechanics, vol.21, issue.3, pp.49-72, 2007.
DOI : 10.1007/s00466-007-0168-8

C. P. Robert and G. Casella, Monte Carlo statistical methods, 2004.

H. Sato, M. C. Fehler, and T. Maeda, Seismic wave propagation and scattering in the heterogeneous earth, 2012.

W. Shi and C. Zhang, Error analysis of generalized polynomial chaos for nonlinear random ordinary differential equations, Applied Numerical Mathematics, vol.62, issue.12, pp.1954-1964, 2012.
DOI : 10.1016/j.apnum.2012.08.007

G. Stefanou, The stochastic finite element method: Past, present and future, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.9-12, pp.9-12, 2009.
DOI : 10.1016/j.cma.2008.11.007

Q. A. Ta, D. Clouteau, and R. Cottereau, Modeling of random anisotropic elastic media and impact on wave propagation, Revue europ??enne de m??canique num??rique, vol.19, issue.1-3, pp.241-253241, 2010.
DOI : 10.3166/ejcm.19.241-253

URL : https://hal.archives-ouvertes.fr/hal-00709537

R. Taherzadeh, D. Clouteau, and R. Cottereau, Simple formulas for the dynamic stiffness of pile groups, Earthquake Engineering & Structural Dynamics, vol.97, issue.SM5, pp.1665-1685, 2009.
DOI : 10.1002/eqe.918

N. E. Wiberg and P. Díez, Adaptive modeling and simulation, Comp. Meth. Appl. Mech. Engr, vol.195, pp.4-6, 2006.

Z. J. Yang, X. T. Su, J. F. Chen, and G. H. Liu, Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials, International Journal of Solids and Structures, vol.46, issue.17, pp.3222-3234, 2009.
DOI : 10.1016/j.ijsolstr.2009.04.013

G. Zhang and M. Gunzburger, Error Analysis of a Stochastic Collocation Method for Parabolic Partial Differential Equations with Random Input Data, SIAM Journal on Numerical Analysis, vol.50, issue.4, pp.1922-1940, 2012.
DOI : 10.1137/11084306X

O. C. Zienkiewicz and J. Z. Zhu, A simple error estimator and adaptive procedure for practical engineerng analysis, International Journal for Numerical Methods in Engineering, vol.7, issue.18, pp.337-357, 1987.
DOI : 10.1002/nme.1620240206