R. A. Adams, Sobolev spaces, Pure and Applied Mathematics, vol.65, 1975.

J. Ahn and D. E. Stewart, Existence of Solutions for a Class of Impact Problems Without Viscosity, SIAM Journal on Mathematical Analysis, vol.38, issue.1, pp.37-63, 2006.
DOI : 10.1137/S0036141004444664

P. Alart and A. Curnier, A generalized newton method for contact problems with friction, J. Mech. Theor. Appl, vol.7, pp.67-82, 1988.
URL : https://hal.archives-ouvertes.fr/hal-01433772

M. Astorino, F. Chouly, and M. A. Fernández, An added-mass free semi-implicit coupling scheme for fluid???structure interaction, Comptes Rendus Mathematique, vol.347, issue.1-2, pp.347-99, 2009.
DOI : 10.1016/j.crma.2008.11.003

URL : https://hal.archives-ouvertes.fr/inria-00542751

R. Becker, P. Hansbo, and R. Stenberg, A finite element method for domain decomposition with non-matching grids, ESAIM: Mathematical Modelling and Numerical Analysis, vol.37, issue.2, pp.209-225, 2003.
DOI : 10.1051/m2an:2003023

URL : https://hal.archives-ouvertes.fr/inria-00073065

S. Brenner and L. Scott, The Mathematical Theory of Finite Element Methods, of Texts in Applied Mathematics, 2007.

H. Brezis, ??quations et in??quations non lin??aires dans les espaces vectoriels en dualit??, Annales de l???institut Fourier, vol.18, issue.1, pp.115-175, 1968.
DOI : 10.5802/aif.280

E. Burman and M. A. Fernández, Stabilization of explicit coupling in fluid???structure interaction involving fluid incompressibility, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.5-8, pp.766-784, 2009.
DOI : 10.1016/j.cma.2008.10.012

URL : https://hal.archives-ouvertes.fr/inria-00247409

G. Choudury and I. Lasiecka, Optimal convergence rates for semidiscrete approximations of parabolic problems with nonsmooth boundary data, Numerical Functional Analysis and Optimization, vol.1054, issue.5-6, pp.469-485, 1991.
DOI : 10.1137/0719002

F. Chouly, An adaptation of Nitsche??s method to the Tresca friction problem, Journal of Mathematical Analysis and Applications, vol.411, issue.1, pp.329-339, 2014.
DOI : 10.1016/j.jmaa.2013.09.019

F. Chouly and P. Hild, A Nitsche-Based Method for Unilateral Contact Problems: Numerical Analysis, SIAM Journal on Numerical Analysis, vol.51, issue.2, pp.1295-1307, 2013.
DOI : 10.1137/12088344X

URL : https://hal.archives-ouvertes.fr/hal-00717711

F. Chouly, P. Hild, and Y. Renard, Symmetric and non-symmetric variants of Nitsche???s method for contact problems in elasticity: theory and numerical experiments, Mathematics of Computation, vol.84, issue.293
DOI : 10.1090/S0025-5718-2014-02913-X

F. Chouly, P. Hild, and Y. Renard, A Nitsche finite element method for dynamic contact. 2. Stability analysis and numerical experiments, Preparation, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01061496

P. G. Ciarlet, Handbook of Numerical Analysis The finite element method for elliptic problems, Lions), vol.II, issue.1, pp.17-352, 1991.

F. Dabaghi, A. Petrov, J. Pousin, and Y. Renard, Convergence of mass redistribution method for the one-dimensional wave equation with a unilateral constraint at the boundary, ESAIM: Mathematical Modelling and Numerical Analysis, vol.48, issue.4, 2014.
DOI : 10.1051/m2an/2013133

C. D. Angelo and P. Zunino, Numerical approximation with Nitsche's coupling of transient Stokes'/Darcy's flow problems applied to hemodynamics, Appl. Numer. Math, vol.62, pp.378-395, 2012.

D. Doyen, A. Ern, and S. Piperno, Time-Integration Schemes for the Finite Element Dynamic Signorini Problem, SIAM Journal on Scientific Computing, vol.33, issue.1, pp.223-249, 2011.
DOI : 10.1137/100791440

URL : https://hal.archives-ouvertes.fr/hal-00440128

C. Eck, J. Jaru?ek, and M. Krbec, Unilateral contact problems, of Pure and Applied Mathematics, 2005.
DOI : 10.1201/9781420027365

A. Ern and J. Guermond, Theory and practice of finite elements, of Applied Mathematical Sciences, 2004.
DOI : 10.1007/978-1-4757-4355-5

R. Glowinski and P. L. Tallec, Augmented Lagrangian and operator-splitting methods in nonlinear mechanics, SIAM Studies in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), vol.9, 1989.
DOI : 10.1137/1.9781611970838

O. Gonzalez, Exact energy and momentum conserving algorithms for general models in nonlinear elasticity, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.13-14, pp.1763-1783, 2000.
DOI : 10.1016/S0045-7825(00)00189-4

URL : https://hal.archives-ouvertes.fr/hal-01363585

W. Han and M. Sofonea, Quasistatic contact problems in viscoelasticity and viscoplasticity, AMSIP Studies in Advanced Mathematics, vol.30, 2002.

A. Hansbo and P. Hansbo, A finite element method for the simulation of strong and weak discontinuities in solid mechanics, Computer Methods in Applied Mechanics and Engineering, vol.193, issue.33-35, pp.3523-3540, 2004.
DOI : 10.1016/j.cma.2003.12.041

P. Hansbo, Nitsche's method for interface problems in computational mechanics, GAMM- Mitt, pp.183-206, 2005.

P. Hansbo, J. Hermansson, and T. Svedberg, Nitsche's method combined with space???time finite elements for ALE fluid???structure interaction problems, Computer Methods in Applied Mechanics and Engineering, vol.193, issue.39-41, pp.4195-4206, 2004.
DOI : 10.1016/j.cma.2003.09.029

J. Haslinger, I. Hlavá?ek, and J. Ne?as, Handbook of Numerical Analysis Numerical methods for unilateral problems in solid mechanics, Ciarlet and J.L. Lions), vol.IV, issue.2, pp.313-385, 1996.

P. Hauret and P. L. Tallec, Energy-controlling time integration methods for nonlinear elastodynamics and low-velocity impact, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.37-40, pp.4890-4916, 2006.
DOI : 10.1016/j.cma.2005.11.005

URL : https://hal.archives-ouvertes.fr/hal-00111458

B. Heinrich and B. Jung, Nitsche mortaring for parabolic initial-boundary value problems, Electron. Trans. Numer. Anal, vol.32, pp.190-209, 2008.

P. Heintz and P. Hansbo, Stabilized Lagrange multiplier methods for bilateral elastic contact with friction, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.33-36, pp.4323-4333, 2006.
DOI : 10.1016/j.cma.2005.09.008

H. B. Khenous, P. Laborde, and Y. Renard, Mass redistribution method for finite element contact problems in elastodynamics, European Journal of Mechanics - A/Solids, vol.27, issue.5, pp.918-932, 2008.
DOI : 10.1016/j.euromechsol.2008.01.001

URL : https://hal.archives-ouvertes.fr/hal-00582045

N. Kikuchi and J. T. Oden, Contact problems in elasticity: a study of variational inequalities and finite element methods, SIAM Studies in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), vol.8, 1988.
DOI : 10.1137/1.9781611970845

J. U. Kim, A boundary thin obstacle problem for a wave equation, Communications in Partial Differential Equations, vol.36, issue.8-9, pp.1011-1026, 1989.
DOI : 10.1080/03605308908820640

URL : https://hal.archives-ouvertes.fr/hal-01330421

T. A. Laursen, Computational contact and impact mechanics, 2002.
DOI : 10.1007/978-3-662-04864-1

G. Lebeau and M. Schatzman, A wave problem in a half-space with a unilateral constraint at the boundary, Journal of Differential Equations, vol.53, issue.3, pp.309-361, 1984.
DOI : 10.1016/0022-0396(84)90030-5

URL : https://hal.archives-ouvertes.fr/hal-01294216

C. Pozzolini, Y. Renard, and M. Salaün, Vibro-impact of a plate on rigid obstacles: existence theorem, convergence of a scheme and numerical simulations, IMA Journal of Numerical Analysis, vol.33, issue.1, pp.261-294, 2013.
DOI : 10.1093/imanum/drr057

URL : https://hal.archives-ouvertes.fr/hal-00812715

Y. Renard, The singular dynamic method for constrained second order hyperbolic equations: Application to dynamic contact problems, Journal of Computational and Applied Mathematics, vol.234, issue.3, pp.906-923, 2010.
DOI : 10.1016/j.cam.2010.01.058

URL : https://hal.archives-ouvertes.fr/hal-01461799

Y. Renard, Generalized Newton???s methods for the approximation and resolution of frictional contact problems in elasticity, Computer Methods in Applied Mechanics and Engineering, vol.256, pp.38-55, 2013.
DOI : 10.1016/j.cma.2012.12.008

R. Stenberg, On some techniques for approximating boundary conditions in the finite element method, International Symposium on Mathematical Modelling and Computational Methods Modelling 94, pp.139-148, 1994.
DOI : 10.1016/0377-0427(95)00057-7

V. Thomée, Galerkin finite element methods for parabolic problems, of Springer Series in Computational Mathematics, 1997.
DOI : 10.1007/978-3-662-03359-3

B. Wohlmuth, Variationally consistent discretization schemes and numerical algorithms for contact problems, Acta Numerica, vol.6, pp.569-734, 2011.
DOI : 10.1016/j.cma.2005.06.003

URL : https://hal.archives-ouvertes.fr/hal-01382364

P. Wriggers and G. Zavarise, A formulation for frictionless contact problems using a weak form introduced by Nitsche, Computational Mechanics, vol.42, issue.1-3, pp.407-420, 2008.
DOI : 10.1007/s00466-007-0196-4