C. Bernardi, A new nonconforming approach to domain decomposition : the mortar element method. Nonliner Partial Differential Equations and Their Applications, 1994.

. Faker-ben and . Belgacem, The mortar finite element method with Lagrange multipliers, Numerische Mathematik, vol.84, issue.2, pp.173-197, 1999.

F. , B. Belgacem, and Y. Maday, A spectral element methodology tuned to parallel implementations, Computer Methods in Applied Mechanics and Engineering, vol.116, issue.1, pp.59-67, 1994.

C. Bernardi, N. Debit, and Y. Maday, Coupling finite element and spectral methods: first results, Mathematics of Computation, vol.54, issue.189, pp.21-39, 1990.
DOI : 10.1090/S0025-5718-1990-0995205-7
URL : http://www.ams.org/mcom/1990-54-189/S0025-5718-1990-0995205-7/S0025-5718-1990-0995205-7.pdf

I. Barbara and . Wohlmuth, Discretization Methods and Iterative Solvers Based on Domain Decomposition, Lecture Notes in Computational Science and Engineering, vol.17, 2001.

I. Babu?ka and J. M. Melenk, THE PARTITION OF UNITY METHOD, International Journal for Numerical Methods in Engineering, vol.9, issue.4, pp.727-758, 1997.
DOI : 10.1007/978-3-642-96379-7

J. Everett and D. , An extended finite element method with discontinuous enrichment for applied mechanics . Northwestern university, 1999.

G. Ferté, N. Massin, and . Moës, Interface problems with quadratic X-FEM: design of a stable multiplier space and error analysis, International Journal for Numerical Methods in Engineering, vol.16, issue.11, pp.834-870, 2014.
DOI : 10.1016/0045-7949(83)90147-5

J. Sethian, Level set methods and fast marching methods : evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science, 1999.

N. Sukumar, L. David, N. Chopp, T. Moës, and . Belytschko, Modeling holes and inclusions by level sets in the extended finite-element method. Computer methods in applied mechanics and engineering, pp.6183-6200, 2001.
DOI : 10.1016/s0045-7825(01)00215-8
URL : https://hal.archives-ouvertes.fr/hal-01007065

A. Michael and . Puso, A 3d mortar method for solid mechanics, International Journal for Numerical Methods in Engineering, vol.59, issue.3, pp.315-336, 2004.

P. Laborde, J. Pommier, Y. Renard, and M. Salaün, High-order extended finite element method for cracked domains, International Journal for Numerical Methods in Engineering, vol.3, issue.3, pp.354-381, 2005.
DOI : 10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N
URL : https://hal.archives-ouvertes.fr/hal-00815711

E. Chahine, Etude mathématique et numérique de méthodes d'éléments finis étendues pour le calcul en domaines fissurés, Thèse de doctorat dirigée par Laborde, Patrick Mathématiques appliquées Toulouse, 2008.

E. Chahine, P. Laborde, and Y. Renard, A non-conformal eXtended Finite Element approach: Integral matching Xfem, Applied Numerical Mathematics, vol.61, issue.3, pp.322-343, 2011.
DOI : 10.1016/j.apnum.2010.10.009
URL : https://hal.archives-ouvertes.fr/hal-00690453

M. Ursula, A. Mayer, A. Popp, . Gerstenberger, A. Wolfgang et al., 3d fluid?structure-contact interaction based on a combined XFEM FSI and dual mortar contact approach, Computational Mechanics, vol.46, issue.1, pp.53-67, 2010.

A. Cuba-ramos, A. M. Aragón, S. Soghrati, H. Philippe, J. Geubelle et al., A new formulation for imposing Dirichlet boundary conditions on non-matching meshes, International Journal for Numerical Methods in Engineering, vol.192, issue.28-30, pp.430-444, 2015.
DOI : 10.1016/S0045-7825(03)00346-3

H. Ben, D. , and G. Rateau, The Arlequin method as a flexible engineering design tool, International journal for numerical methods in engineering, vol.62, issue.11, pp.1442-1462, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00018915

F. Tony, . Chan, P. Tarek, and . Mathew, Domain decomposition algorithms, Acta numerica, vol.3, pp.61-143, 1994.

F. B. Belgacem, P. Hild, and P. Laborde, The mortar finite element method for contact problems, Recent Advances in Contact Mechanics, pp.263-271, 1998.
DOI : 10.1016/S0895-7177(98)00121-6

K. A. Fischer and P. Wriggers, Frictionless 2D Contact formulations for finite deformations based on the mortar method, Computational Mechanics, vol.1, issue.3, pp.226-244, 2005.
DOI : 10.1007/s00466-005-0660-y

A. Kathrin, P. Fischer, and . Wriggers, Mortar based frictional contact formulation for higher order interpolations using the moving friction cone, Computer Methods in Applied Mechanics and Engineering, vol.195, pp.37-405020, 2006.

A. Popp, Mortar Methods for Computational Contact Mechanics and General Interface Problems. Dissertation
DOI : 10.1002/gamm.201410004
URL : https://onlinelibrary.wiley.com/doi/pdf/10.1002/gamm.201410004

A. Vladislav and . Yastrebov, Numerical methods in contact mechanics, ISTE, 2013.

P. Wriggers, Finite element algorithms for contact problems, Archives of Computational Methods in Engineering, vol.33, issue.4, pp.1-49
DOI : 10.1137/1.9781611970845

N. Sukumar and T. Belytschko, Arbitrary branched and intersecting cracks with the extended finite element method, Int. J. Numer. Meth. Eng, vol.48, pp.1741-1760, 2000.
URL : https://hal.archives-ouvertes.fr/hal-01005274