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.1111-1129, 1984.
DOI : 10.1002/nme.1620200611

M. Paraschivoiu, J. Peraire, and A. T. Patera, A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations, Computer Methods in Applied Mechanics and Engineering, vol.150, issue.1-4, pp.1-4289, 1997.
DOI : 10.1016/S0045-7825(97)00086-8

R. Rannacher and F. Suttmeier, 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

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, issue.1-4, pp.351-362, 1998.
DOI : 10.1016/S0045-7825(97)00220-X

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, issue.1-4, pp.1-4313, 1999.
DOI : 10.1016/S0045-7825(98)00343-0

P. Ladevèze, P. Rougeot, P. Blanchard, and J. P. Moreau, Local error estimators for finite element linear analysis, Computer Methods in Applied Mechanics and Engineering, vol.176, issue.1-4, pp.1-4231, 1999.
DOI : 10.1016/S0045-7825(98)00339-9

T. Strouboulis, I. Babu?ka, D. K. Datta, K. Copps, and S. K. 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.1-3261, 2000.
DOI : 10.1016/S0045-7825(99)00077-8

R. Becker and R. Rannacher, An optimal control approach to a posteriori error estimation in finite element methods, Acta Numerica, vol.10, pp.1-120, 2001.
DOI : 10.1017/S0962492901000010

N. Parés, J. Bonet, A. Huerta, and J. Peraire, The computation of bounds for linear-functional outputs of weak solutions to the two-dimensional elasticity equations, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.4-6, pp.4-6406, 2006.
DOI : 10.1016/j.cma.2004.10.013

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 : 10.1002/nme.1705
URL : https://hal.archives-ouvertes.fr/hal-00109713

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.181, issue.12, pp.711387-1411, 2007.
DOI : 10.1002/nme.1978

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, issue.9-12, pp.9-12994, 2008.
DOI : 10.1016/j.cma.2007.09.021

P. Ladevèze, Strict upper error bounds on computed outputs of interest in computational structural mechanics, Computational Mechanics, vol.176, issue.4???6, pp.271-286, 2008.
DOI : 10.1007/s00466-007-0201-y

P. Ladevèze and J. Waeytens, Model verification in dynamics through strict upper error bounds, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.21-26, pp.21-261775, 2009.
DOI : 10.1016/j.cma.2008.12.020

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.45, issue.12, pp.671-700, 2010.
DOI : 10.1002/nme.2623

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.328, issue.5, pp.1638-1664, 2010.
DOI : 10.1002/nme.2957

L. Chamoin and P. Ladevèze, Strict and practical bounds through a non-intrusive and goal-oriented error estimation method for linear viscoelasticity problems. Finite Elements in Analysis and Design, pp.251-262, 2009.

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

N. Parés, P. Díez, and A. Huerta, Subdomain-based flux-free a posteriori error estimators, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.4-6, pp.4-6297, 2006.
DOI : 10.1016/j.cma.2004.06.047

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.195, issue.4-6, pp.1493-1516, 2009.
DOI : 10.1002/nme.2441

R. Cottereau, P. Díez, and A. Huerta, Strict error bounds for linear solid mechanics problems using a subdomain-based flux-free method, Computational Mechanics, vol.71, issue.2, pp.533-547, 2009.
DOI : 10.1007/s00466-009-0388-1
URL : https://hal.archives-ouvertes.fr/hal-00396420

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/nme.2496

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.199, issue.9-12, pp.766-777, 2010.
DOI : 10.1016/j.cma.2009.11.007

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.46, issue.4-6, pp.409-441, 2011.
DOI : 10.1002/nme.3180
URL : https://hal.archives-ouvertes.fr/hal-01056705

F. Pled, L. Chamoin, and P. Ladevèze, An enhanced method with local energy minimization for the robust a posteriori construction of equilibrated stress fields in finite element analyses, Computational Mechanics, vol.24, issue.2, pp.357-378, 2012.
DOI : 10.1007/s00466-011-0645-y
URL : https://hal.archives-ouvertes.fr/hal-01056871

T. Strouboulis, I. Babu?ka, and K. Copps, The design and analysis of the Generalized Finite Element Method, Computer Methods in Applied Mechanics and Engineering, vol.181, issue.1-3, pp.43-69, 2000.
DOI : 10.1016/S0045-7825(99)00072-9

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 : 10.1002/nme.228

P. Ladevèze, P. Marin, J. P. Pelle, and J. L. Gastine, Accuracy and optimal meshes in finite element computation for nearly incompressible materials, Computer Methods in Applied Mechanics and Engineering, vol.94, issue.3, pp.303-315, 1992.
DOI : 10.1016/0045-7825(92)90057-Q

W. Prager and J. L. Synge, Approximations in elasticity based on the concept of function space, Quarterly of Applied Mathematics, vol.5, issue.3, pp.261-269, 1947.
DOI : 10.1090/qam/25902

M. W. Steklov, Sur lesprobì emes fondamentaux de la physique mathématique. Annales Scientifiques de l' ´ Ecole Normale Supérieure, pp.455-490, 1902.

J. Ladevèze and P. Ladevèze, Upper bounds of the Poincaré constant in elasticity (in french) Rendiconti Accademia Nazionale dei Lincei, Serie VIII, pp.548-556, 1978.

C. Hochard, P. Ladevèze, and L. Proslier, A simplified analysis of elastic structures, European Journal of Mechanics Solids, vol.12, pp.509-535, 1993.

C. Hochard and L. Proslier, A simplified analysis of plate structures using Trefftz-functions, International Journal for Numerical Methods in Engineering, vol.20, issue.1, pp.179-195, 1992.
DOI : 10.1002/nme.1620340111

R. D. Mindlin, Force at a point in the interior of a semi-infinite solid, Journal of Physics, vol.7, issue.5, pp.195-202, 1936.

R. D. Mindlin and D. H. Cheng, Nuclei of Strain in the Semi???Infinite Solid, Journal of Applied Physics, vol.21, issue.9, pp.926-930, 1950.
DOI : 10.1063/1.1699785

©. Copyright, Prepared using nmeauth, cls DOI: 10.1002/nme 36 P. LADEV`EZELADEV` LADEV`EZE, F. PLED AND L. CHAMOIN, 2012.

K. F. Graff, Wave Motion in Elastic Solids, 1975.

S. Vijayakumar and D. E. Cormack, Green???s Functions for the Biharmonic Equation: Bonded Elastic Media, SIAM Journal on Applied Mathematics, vol.47, issue.5, pp.982-997, 1987.
DOI : 10.1137/0147065

M. Stern, E. B. Becker, and R. S. Dunham, A contour integral computation of mixed-mode stress intensity factors, International Journal of Fracture, vol.12, issue.10, pp.359-368, 1007.

J. Panetier, P. Ladevèze, and F. Louf, Strict bounds for computed stress intensity factors, Computers & Structures, vol.87, issue.15-16, pp.15-161015, 2009.
DOI : 10.1016/j.compstruc.2008.11.014
URL : https://hal.archives-ouvertes.fr/hal-00101778

E. Trefftz, Ein Gegenstück zum Ritzschen Verfahren, Proceedings of the 2nd International Congress of Applied Mechanics, pp.131-137, 1926.

E. Kita and N. Kamiya, Trefftz method: an overview Advances in Engineering Software, pp.3-12, 1995.

A. Zieli´nskizieli´nski, On trial functions applied in the generalized Trefftz method Advances in Engineering Software, pp.147-155, 1995.

V. Kompi?, M. Toma, M. Zmindák, and M. Handrik, Use of Trefftz functions in non-linear BEM/FEM, Computers & Structures, vol.82, issue.27, pp.2351-2360, 2004.
DOI : 10.1016/j.compstruc.2004.04.006

V. Kompi?, M. Stiavnick´ystiavnick´y, M. Kompi?, and M. ?. Zmindák, Trefftz interpolation based multi-domain boundary point method, Engineering Analysis with Boundary Elements, vol.29, issue.4, pp.391-396, 2005.
DOI : 10.1016/j.enganabound.2004.06.007

A. Zieli´nskizieli´nski and O. C. Zienkiewicz, Generalized finite element analysis with T-complete boundary solution functions, International Journal for Numerical Methods in Engineering, vol.IV, issue.3, pp.509-528, 1985.
DOI : 10.1002/nme.1620210310

J. Sladek, V. Sladek, V. Kompi?, and R. Van-keer, Application of multi-region Trefftz method in elasticity, CMES- Computer Modeling in Engineering & Sciences, vol.1, issue.4, pp.1-8, 2000.

J. Sladek and V. Sladek, A Trefftz function approximation in local boundary integral equations, Computational Mechanics, vol.28, issue.3-4, pp.212-219, 2002.
DOI : 10.1007/s00466-001-0282-y