S. Descombes, S. Lanteri, and L. Moya, Locally implicit time integration strategies in a discontinuous Galerkin method for Maxwell's equations, vol.56, pp.190-218, 2013.

V. Dolean, H. Fahs, L. Fezoui, and S. Lanteri, Locally implicit discontinuous Galerkin method for time domain electromagnetics, Journal of Computational Physics, vol.229, issue.2, pp.512-526, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00403741

T. Rylander, Stability of Explicit-Implicit Hybrid Time-Stepping Schemes for Maxwell's Equations, Journal of Computational Physics, vol.179, issue.2, pp.426-438, 2002.

M. Hochbruck and A. Sturm, Upwind discontinuous Galerkin space discretisation and locally implicit time integration for linear Maxwell's equations, Mathematics of Computation, pp.1-33, 2018.

M. Hochbruck and A. Sturm, Error analysis of a second-order locally implicit method for linear Maxwell's equations, SIAM Journal of Numerical Analysis, vol.54, issue.5, pp.3167-3191, 2016.

J. Chabassier and S. Imperiale, Fourth order energy-preserving locally implicit time discretisation for linear wave equations, International Journal for Numerical Methods in Engineering, vol.106, issue.8, 2015.

M. J. Grote, M. Mehlin, and S. Sauter, Convergence analysis of energy conserving explicit local time-stepping methods for the wave equation, SIAM Journal of numerical analysis, vol.56, issue.2, pp.994-1021, 2018.

J. Diaz and M. J. , Grote Energy conserving explicit local time-stepping for second-order wave equations, SIAM Journal of Scientific Computing, vol.31, 1985.

G. Derveaux, P. Joly, and J. Rodríguez, Effective computational methods for wave propagation, Space time mesh refinement methods, vol.13, 2008.

J. Rodríguez, A spurious-free space-time mesh refinement for elastodynamics, International Journal For Multiscale Computational Engineering, vol.6, issue.3, pp.263-279, 2008.

M. Dumbser, M. Käser, and E. F. Toro, An arbitrary high-order Discontinuous Galerkin method for elastic waves on unstructured meshes -V. Local time stepping and p-adaptivity, Geophysical Journal International, vol.171, pp.695-717, 2007.

F. Collino, T. Fouquet, and P. Joly, A conservative space-time mesh refinement method for the 1-d wave equation. Part I: Construction, Numerische Mathematik, vol.95, issue.2, pp.197-221, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00989055

J. Chabassier and S. Imperiale, Space/Time convergence analysis of a class of conservative schemes for linear wave equations, Comptes Rendus Mathématique, vol.355, issue.3, pp.282-289, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01421882

R. Dautray and J. , and 6 -Evolution Problems I and II, Lions. Mathematical Analysis and Numerical Methods for Science and Technology, vol.5, 2000.

G. Cohen, P. Joly, J. E. Roberts, and N. Tordjman, Higher-order triangular finite elements with mass lumping for the wave equation, SIAM, J. Numer. Anal, vol.38, issue.6, pp.2047-2078, 2001.
URL : https://hal.archives-ouvertes.fr/hal-01010373

G. Cohen, P. Joly, and N. Tordjman, Higher-order finite elements with mass-lumping for the 1D wave equation, Finite Element Analysis and Design, vol.16, issue.3, pp.32-336, 1994.

G. Cohen, Higher-order numerical methods for transient wave equations, 2001.
URL : https://hal.archives-ouvertes.fr/hal-01166961

Y. Maday and A. Patera, Spectral element methods for the incompressible Navier-Stokes equations, State-ofthe-art surveys on computational mechanics, 1989.

Y. Maday, C. Mavriplis, and A. T. Patera, Nonconforming mortar element methods -Application to spectral discretisations in Domain decomposition methods, pp.392-418, 1989.

J. Albella, H. B. Dhia, ,. S. Imperiale, and J. Rodríguez, Mathematical and Numerical Study of Transient Wave Scattering by Obstacles with a New Class of Arlequin Coupling, SIAM Journal on Numerical Analysis, vol.57, issue.5, pp.2436-2468, 2019.

J. C. Gilbert and P. Joly, Higher order time stepping for second order hyperbolic problems and optimal CFL conditions, Partial Differential Equations, vol.16, pp.67-93, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00976773

P. Joly and J. Rodríguez, Optimized higher order time discretisation of second order hyperbolic problems: construction and numerical study, Journal of Computational and Applied Mathematics, vol.234, issue.6, 2010.

F. Brezzi and M. Fortin, Mixed and hybrid finite element methods, vol.15, 2012.

P. J. Van-der-houwen and B. P. Sommeijer, On the Internal Stability of Explicit, m-Stage Runge-Kutta Methods for Large m-Values, Journal of Applied Mathematics and Mechanics, vol.60, issue.10, 1980.

W. Hundsdorfer and J. G. Verwer, Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, Springer Series in Computational Mathematics, 2003.

E. Bécache and P. Joly, Space-time mesh refinement for elastodynamics, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.2-5, pp.355-366, 2005.

P. Joly and J. Rodríguez, An error analysis of conservative space-time mesh refinement methods for the onedimensional wave equation, SIAM Journal on Numerical Analysis, vol.43, issue.2, pp.825-859, 2005.

J. Rodríguez, Une nouvelle méthode de raffinement de maillage spatio-temporel pour l'équation des ondes, Comptes Rendus Mathématique. Académie des Sciences. Paris, vol.339, issue.6, pp.445-450, 2004.

M. Hochbruck and A. Sturm, On leap-frog-Chebyshev schemes, 2018.

M. J. Grote and T. Mitkova, Explicit local time-stepping methods for Maxwell's equations, Journal of Computational and Applied Mathematics, vol.234, issue.12, pp.3283-3302, 2010.

J. Diaz and M. J. Grote, Multi-level explicit local time-stepping methods for second-order wave equations, Computer Methods in Applied Mechanics and Engineering, vol.291, pp.240-265, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01184090

F. Collino, T. Fouquet, and P. Joly, A conservative space-time mesh refinement method for the 1-D wave equation, Numerische Mathematik, vol.95, issue.2, pp.223-251, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00989055

E. Bécache, J. Rodríguez, and C. Tsogka, Convergence results of the fictitious domain method for a mixed formulation of the wave equation with a Neumann boundary condition, ESAIM: Mathematical Modelling and Numerical Analysis, vol.43, issue.2, pp.377-398, 2009.

B. I. Wohlmuth, A Mortar Finite Element Method Using Dual Spaces for the Lagrange Multiplier, SIAM Journal on Numerical Analysis, vol.38, issue.3, pp.989-1012, 2000.

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

J. Chabassier, J. Diaz, and S. Imperiale, Construction and analysis of fourth order, energy consistent, family of explicit time discretizations for dissipative linear wave equations, ESAIM: Mathematical Modelling and Numerical Analysis, vol.54, pp.845-878, 2020.
URL : https://hal.archives-ouvertes.fr/hal-01894238

M. Durufle, P. Grob, and P. Joly, Influence of Gauss and Gauss-Lobatto quadrature rules on the accuracy of a quadrilateral finite element method in the time domain, Numerical Methods for Partial Differential Equations, vol.25, pp.526-551, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00403791