I. Babu?-ska and T. Strouboulis, The finite element method and its reliability, 2001.

I. Babu?-ska, 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.

R. Becker and R. Rannacher, An optimal control approach to shape a posteriori error estimation in finite element methods, Acta Numerica, pp.1-120, 2001.

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

L. Chamoin and P. Ladevèze, Bounds on history-dependent or independent local quantities in viscoelasticity problems solved by approximate methods, International Journal for Numerical Methods in Engineering, vol.71, issue.12, pp.1387-1411, 2007.

L. Chamoin and P. Ladevèze, A non-intrusive method for the calculation of strict and efficient bounds of calculated outputs of interest in linear viscoelasticity problems, Computer Methods in Applied Mechanics and Engineering, vol.197, pp.9-12994, 2008.

F. Cirak and E. Ramm, A posteriori error estimation and adaptivity for linear elasticity using the reciprocal theorem, Computer Methods in Applied Mechanics and Engineering, vol.156, pp.351-362, 1998.

R. Cottereau, P. Diez, and A. Huerta, Strict error bounds for linear solid mechanics problems using a subdomain-based flux-free method, Computational Mechanics, vol.44, issue.4, pp.533-547, 2009.
DOI : 10.1007/s00466-009-0388-1
URL : https://hal.archives-ouvertes.fr/hal-00396420

D. M. Babuska, I. Oden, and J. T. , Solution of stochastic partial differential equations using Galerkin finite element techniques, Computer Methods in Applied Mechanics and Engineering, vol.190, pp.6359-6372, 2001.

E. Florentin, L. Gallimard, and J. P. Pelle, Evaluation of the local quality of stresses in 3D finite element analysis, Computer Methods in Applied Mechanics and Engineering, vol.191, pp.4441-4457, 2002.

E. Florentin, L. Gallimard, P. J. , and R. Ph, Adaptive meshing for local quality of FE stresses, Engineering Computations, vol.22, pp.149-164, 2005.

E. Florentin, P. Ladevèze, and J. Bellec, Error bounds on outputs of interest for linear stochastic problems, Proceedings of the 3rd European Conference on Computational Mechanics, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00079586

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

R. Ghanem and M. Pelissetti, Error estimation for the validation of model-based predictions, Proceedings of the 5th World Congress on Computational Mechanics, 2002.

A. N. Kolmogorov, Foundations of the Theory of Probability, 1956.

P. Ladevèze, Validation and verification of stochastic models in uncertain environment using constitutive relation error method, Technical Report, vol.258, 2003.

P. Ladevèze, Strict upper error bounds for calculated outputs of interest in computational structural mechanics, Computational Mechanics, vol.42, issue.2, pp.271-286, 2008.

P. Ladevèze and J. Pelle, Mastering Calculations in Linear and Nonlinear Mechanics, 2004.

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, pp.225-234, 2006.

P. Ladevèze, L. Chamoin, and E. Florentin, A new non-intrusive technique for the construction of admissible stress fields in model verification, Computer Methods in Applied Mechanics and Engineering, vol.2010, issue.199, pp.9-12766

P. Ladevèze and J. Waeytens, Model verification in dynamics through strict upper error bounds, Computer Methods in Applied Mechanics and Engineering, vol.198, pp.21-261775, 2009.

P. Ladevèze and L. Chamoin, Calculation of strict error bounds for finite element approximations of non-linear pointwise quantities of interest, International Journal for Numerical Methods in Engineering, vol.84, pp.1638-1664, 2010.

H. G. Matthies and C. G. Bucher, Finite element for stochastic media problems, Computer Methods in Applied Mechanics and Engineering, vol.168, pp.3-17, 1999.

J. P. Moitinho-de-almeida and E. A. Maunder, Recovery of equilibrium on star patches using a partition of unity technique, International Journal for Numerical Methods in Engineering, vol.79, pp.1493-1516, 2009.

J. T. Oden, I. Babu?-ska, F. Nobile, Y. Feng, and R. Tempone, Theory and methodology for estimation and control of error due to modeling, approximation, and uncertainty, Computer Methods in Applied Mechanics and Engineering, vol.194, pp.195-204, 2005.

J. Panetier, P. Ladevèze, and L. Chamoin, Strict and effective bounds in goal-oriented error estimation applied to fracture mechanics problems solved with XFEM, International Journal for Numerical Methods in Engineering, vol.81, pp.671-700, 2010.

M. Paraschivoiu, J. Peraire, and P. A. , A posteriori finite element bounds for linear functional outputs of elliptic partial differential equations, Computer Methods in Applied Mechanics and Engineering, vol.150, pp.289-312, 1997.

N. Pares, P. Diez, and A. Huerta, Subdomain-based flux-free a posteriori error estimators, Computer Methods in Applied Mechanics and Engineering, vol.195, pp.4-6297, 2006.

J. Peraire and P. A. , Bounds for linear-functional outputs of coercive partial differential equations; local indicators and adaptive refinements, Advances in Adaptive Computational Methods in Mechanics (Ladevèze and Oden Editors, pp.199-216, 1998.

F. Pled, L. Chamoin, and P. Ladevèze, On the techniques for constructing admissible stress fields in model verification: performances on engineering examples, International Journal for Numerical Methods in Engineering, vol.88, issue.5, pp.409-441, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01056705

E. Florentin, S. Guinard, and P. Pasquet, A simple estimator for stress errors dedicated to large elastic finite element simulations : Locally reinforced stress construction. Engineering Computations, pp.76-92, 2011.

E. Florentin and G. Lubineau, Identification of the parameters of an elastic material model using the Constitutive Equation Gap Method, Computational Mechanics, vol.46, pp.521-531, 2010.

S. Prudhomme and J. T. Oden, On goal-oriented error estimation for elliptic problems: application to the control of pointwise errors, Computer Methods in Applied Mechanics and Engineering, vol.176, pp.313-331, 1999.

A. Romkes, J. T. Oden, and K. Vemaganti, Multiscale goal-oriented adaptive modeling of random heterogeneous materials, Mechanics of Materials, vol.38, pp.859-872, 2006.

G. Schueller, A state-of-the-art report on computational stochastic mechanics, Probabilistic Engineering Mechanics, vol.12, pp.197-321, 1997.

B. Sudret, M. Berveiller, and M. Lemaire, Eléments finis stochastiques enélasticitéenélasticité linéaire. Comptes Rendus de l'Académie des Sciences, Mécanique, vol.332, pp.531-537, 2004.

E. Stein, S. Ohmnimus, and E. Walhorn, Local error estimates of fem for displacements and stresses in linear elasticity by solving local Neumann problems, International Journal for Numerical Methods in Engineering, vol.52, pp.727-746, 2001.

G. Stefanou, The stochastic finite element method: Past, present and future, Computer Methods in Applied Mechanics and Engineering, vol.198, pp.1031-1051, 2009.