I. Babu?ka 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.1111-1140, 1982.
DOI : 10.1002/nme.1620200611

I. Babu?ka and W. Rheinboldt, A-posteriori error estimates for the finite element method, International Journal for Numerical Methods in Engineering, vol.15, issue.10, pp.1597-615, 1978.
DOI : 10.1002/nme.1620121010

I. Babu?ka, T. Strouboulis, S. Gangaraj, K. Copps, and D. Datta, A-posteriori estimation of the error in the error estimate, Advances in Adaptive Computational Methods in Mechanics, Studies in Applied Mechanics 47, pp.155-97, 1998.
DOI : 10.1016/S0922-5382(98)80010-X

I. Babu?ka, T. Strouboulis, C. Upadhyay, and S. Gangaraj, A posteriori estimation and adaptive control of the pollution error in theh-version of the finite element method, International Journal for Numerical Methods in Engineering, vol.52, issue.24, pp.4207-4242, 1995.
DOI : 10.1108/eb023827

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

E. Florentin, L. Gallimard, and J. Pelle, Evaluation of the local quality of stresses in 3D finite element analysis, Computer Methods in Applied Mechanics and Engineering, vol.191, issue.39-40, pp.4441-57, 2002.
DOI : 10.1016/S0045-7825(02)00389-4

URL : https://hal.archives-ouvertes.fr/hal-01689638

E. Florentin, L. Gallimard, P. Ladevèze, J. Pelle, and P. Rougeot, Local constitutive relation error for mises stress in 3D elasticity, Proc. of ADMOS 2003 -ECCOMAS Thematic Conference, 2003.

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

P. Heintz, P. Larsson, P. Hansbo, and K. Runesson, On adaptive strategies and error control in fracture mechanics, Computers & Structures, vol.82, issue.6, pp.2002-2016, 2002.
DOI : 10.1016/j.compstruc.2003.10.013

URL : http://www.phi.chalmers.se/pub/preprints/ps/phiprint-2002-14.ps

P. Heintz and K. Samuelsson, On adaptive strategies and error control in fracture mechanics, Computers & Structures, vol.82, issue.6, pp.485-97, 2004.
DOI : 10.1016/j.compstruc.2003.10.013

URL : http://www.phi.chalmers.se/pub/preprints/ps/phiprint-2002-14.ps

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

P. Ladevèze and J. Pelle, Méthode de calcul par encadrement des fréquencies propres de structures e ´lastiques, Comptes Rendus Acad. Sci. Paris, Série II, vol.296, pp.1757-60, 1983.

P. Ladevèze and P. Rougeot, New advances on a posteriori error on constitutive relation in f.e. analysis, Computer Methods in Applied Mechanics and Engineering, vol.150, issue.1-4, pp.239-288, 1997.
DOI : 10.1016/S0045-7825(97)00089-3

P. Ladevèze, J. Pelle, and P. Rougeot, ERROR ESTIMATION AND MESH OPTIMIZATION FOR CLASSICAL FINITE ELEMENTS, Engineering Computations, vol.8, issue.1, pp.69-80, 1991.
DOI : 10.1002/nme.1620240206

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.231-277, 1999.
DOI : 10.1016/S0045-7825(98)00339-9

J. Oden and S. Prudhomme, Estimation of Modeling Error in Computational Mechanics, Journal of Computational Physics, vol.182, issue.2, pp.496-515, 2002.
DOI : 10.1006/jcph.2002.7183

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.727-773, 2001.
DOI : 10.1090/S0025-5718-1985-0777265-X

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

W. Prager and J. Synge, Approximations in elasticity based on the concept of function space, Quarterly of Applied Mathematics, vol.5, issue.3, pp.261-270, 1947.
DOI : 10.1090/qam/25902

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.313-344, 1999.
DOI : 10.1016/S0045-7825(98)00343-0

S. Prudhomme, J. Oden, T. Westermann, J. Bass, and M. E. Botkin, Practical methods fora posteriori error estimation in engineering applications, International Journal for Numerical Methods in Engineering, vol.47, issue.8, pp.1193-224, 2003.
DOI : 10.1002/9781118032824

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.434-480, 1997.
DOI : 10.1007/s004660050191

R. Rannacher and F. Stuttmeier, A posteriori error control and mesh adaptation for f.e. models in elasticity and elastoplasticity, Advances in Adaptive Computational Methods in Mechanics, pp.275-92, 1998.

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.251-78, 2006.
DOI : 10.1016/j.cma.2004.05.032

T. Strouboulis, I. Babu?ka, D. Datta, K. Copps, and S. Gangaraj, A posteriori estimation and adaptative control of the error in the quantity of interest part 1: a posteriori estimation of the error in the Von Mises stress and the stress intensity factor, Comp. Meth. in Applied Mech. and Engrg, vol.180, pp.261-74, 2000.

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.337-57, 1987.
DOI : 10.1016/B978-0-12-747255-3.50049-6

E. Further-reading-florentin, L. Gallimard, and J. Pelle, Etude de la qualité locale de différentes versions de l'estimateur d'erreur en relation de comportement, Revue européenne des e ´léments finis, pp.761-83, 2003.

L. Corresponding-author, Gallimard can be contacted at: laurent.gallimard@u-paris10.fr To purchase reprints of this article please e-mail: reprints@emeraldinsight.com Or visit our web site for further details: www