O. Ditlevsen and H. Madsen, Structural Reliability Methods, 1996.

A. Hasofer and N. Lind, An exact and invariant first order reliability format, Journal of Engineering Mechanics (ASCE), vol.100, issue.EM1, pp.111-121, 1974.

I. Babu?-ska and W. 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

P. Ladevèze and D. Leguillon, Error Estimate Procedure in the Finite Element Method and Applications, SIAM Journal on Numerical Analysis, vol.20, issue.3, pp.485-509, 1983.
DOI : 10.1137/0720033

O. Zienkiewicz and J. 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 : 10.1016/B978-0-12-747255-3.50049-6

I. Babu?-ska and A. Miller, The post-processing approach in the finite element method???Part 2: The calculation of stress intensity factors, International Journal for Numerical Methods in Engineering, vol.9, issue.6, pp.1111-1129, 1982.
DOI : 10.1002/nme.1620200611

D. Kelly and J. Isles, Procedures for residual equilibration and local error estimation in the finite element method, Communications in Applied Numerical Methods, vol.19, issue.18, pp.497-505, 1989.
DOI : 10.1002/cnm.1630050803

R. Rannacher and F. Stuttmeier, A feed-back approach to error control in finite element methods: application to linear elasticity, Computational Mechanics, vol.19, issue.5, pp.434-446, 1997.
DOI : 10.1007/s004660050191

J. Peraire and A. Patera, Bounds for Linear???Functional Outputs of Coercive Partial Differential Equations : Local Indicators and Adaptive Refinement, Advances in Adaptive Computational Methods, pp.199-216, 1998.
DOI : 10.1016/S0922-5382(98)80011-1

S. Prudhomme and J. 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, issue.1-4, pp.313-331, 1999.
DOI : 10.1016/S0045-7825(98)00343-0

P. Ladevèze, P. Rougeot, P. Blanchard, and J. Moreau, Local error estimators for finite element linear analysis, Computer Methods in Applied Mechanics and Engineering, vol.176, issue.1-4, pp.231-246, 1999.
DOI : 10.1016/S0045-7825(98)00339-9

S. Ohnimus, E. Stein, 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.4, issue.7, pp.727-746, 2001.
DOI : 10.1090/S0025-5718-1985-0777265-X

S. Prudhomme, J. Oden, T. Westermann, J. Bass, and M. Botkin, Practical methods fora posteriori error estimation in engineering applications, International Journal for Numerical Methods in Engineering, vol.47, issue.8, pp.1193-1224, 2003.
DOI : 10.1002/9781118032824

L. Gallimard and J. Panetier, Error estimation of stress intensity factors for mixed-mode cracks, International Journal for Numerical Methods in Engineering, vol.12, issue.3, pp.299-316, 2006.
DOI : 10.1115/1.3629665
URL : https://hal.archives-ouvertes.fr/hal-00109713

L. Gallimard, 2???norm of the stress for linear elasticity problems, Engineering Computations, vol.23, issue.8, pp.876-897, 2006.
DOI : 10.3166/reef.12.761-783
URL : https://hal.archives-ouvertes.fr/hal-01689784

M. Deb, I. Babuska, 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, 2001.
DOI : 10.1016/S0045-7825(01)00237-7

P. Ladeveze 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
URL : https://hal.archives-ouvertes.fr/hal-00111753

Y. Zhang, D. Kiureghian, and A. , Two Improved Algorithms for Reliability Analysis, Proceedings of the Sixth IFIP WG7.5 Reliability and Optimization of Structural System, 1994.
DOI : 10.1007/978-0-387-34866-7_32

L. Wang and R. Grandhi, Safety index calculation using intervening variables for structural reliability analysis, Computers & Structures, vol.59, issue.6, pp.1139-1148, 1996.
DOI : 10.1016/0045-7949(96)00291-X

D. Kiureghian, A. Dakessian, and T. , Multiple design points in first and second-order reliability, Structural Safety, vol.20, issue.1, pp.37-49, 1998.
DOI : 10.1016/S0167-4730(97)00026-X

J. Mitteau, Error evaluations for the computation of failure probability in static structural reliability problems, Probabilistic Engineering Mechanics, vol.14, issue.1-2, pp.115-119, 1999.
DOI : 10.1016/S0266-8920(98)00022-8

A. Mohamed, M. Lemaire, J. Mitteau, and E. Meister, Finite element and reliability: a method for compound variables???application on a cracked heating system, Nuclear Engineering and Design, vol.185, issue.2-3, pp.185-202, 1998.
DOI : 10.1016/S0029-5493(98)00184-8

M. Pendola, M. A. Lemaire, M. Hornet, and P. , Combination of finite element and reliability methods in nonlinear fracture mechanics, Reliability Engineering & System Safety, vol.70, issue.1, pp.15-27, 2000.
DOI : 10.1016/S0951-8320(00)00043-0

R. Rackwitz and B. Fiessler, Structural reliability under combined random load sequences, Computers & Structures, vol.9, issue.5, pp.484-494, 1979.
DOI : 10.1016/0045-7949(78)90046-9

D. Kiureghian, A. De-stefano, and M. , Efficient Algorithm for Second???Order Reliability Analysis, Journal of Engineering Mechanics, vol.117, issue.12, pp.37-49, 1991.
DOI : 10.1061/(ASCE)0733-9399(1991)117:12(2904)

T. Haukaas, D. Kiureghian, and A. , Strategies for finding the design point in non-linear finite element reliability analysis, Probabilistic Engineering Mechanics, vol.21, issue.2, pp.133-147, 2006.
DOI : 10.1016/j.probengmech.2005.07.005

T. Strouboulis, I. Babu?-ska, D. Datta, K. Copps, and S. Gangaraj, A posteriori estimation and adaptive control of the error in the quantity of interest. Part I: A posteriori estimation of the error in the von Mises stress and the stress intensity factor, Computer Methods in Applied Mechanics and Engineering, vol.181, issue.1-3, pp.261-274, 2000.
DOI : 10.1016/S0045-7825(99)00077-8

R. Beckers and R. Rannacher, An optimal control approach to a posteriori error estimation in finite element methods, Acta Numerica, vol.10, pp.1-102, 2001.
DOI : 10.1017/S0962492901000010

P. Heintz and P. Samuelsson, On adaptive strategies and error control in fracture mechanics, Computers & Structures, vol.82, issue.6, pp.485-497, 2004.
DOI : 10.1016/j.compstruc.2003.10.013
URL : http://www.phi.chalmers.se/pub/preprints/ps/phiprint-2002-14.ps

M. Ruter and E. Stein, Goal-oriented a posteriori error estimates in linear elastic fracture mechanics, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.4-6, pp.251-278, 2006.
DOI : 10.1016/j.cma.2004.05.032

L. Gallimard, A constitutive relation error estimator based on traction-free recovery of the equilibrated stress, International Journal for Numerical Methods in Engineering, vol.23, issue.7-8, pp.460-482, 2009.
DOI : 10.1002/9781118032824
URL : https://hal.archives-ouvertes.fr/hal-01689801

M. Stern, E. Becker, and R. Dunham, A contour integral computation of mixed-mode stress intensity factors, International Journal of Fracture, vol.12, issue.3, pp.359-368, 1976.

H. Tada, P. Paris, and G. Irwin, The Stress Analysis of Crack Handbook, 1985.