F. Ihlenburg and I. Babuska, Finite element solution of the Helmholtz equation with high wave number Part I: The h-version of the FEM, Computers & Mathematics with Applications, vol.30, issue.9, pp.9-37, 1995.
DOI : 10.1016/0898-1221(95)00144-N

X. Feng and H. Wu, Discontinuous Galerkin Methods for the Helmholtz Equation with Large Wave Number, SIAM Journal on Numerical Analysis, vol.47, issue.4, pp.2872-2896, 2009.
DOI : 10.1137/080737538

J. M. Melenk, A. Parsania, and S. Sauter, General DG-Methods for Highly Indefinite Helmholtz Problems, Journal of Scientific Computing, vol.28, issue.4, pp.536-581, 2013.
DOI : 10.1090/S0025-5718-1974-0373326-0

M. Ainsworth, Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods, Journal of Computational Physics, vol.198, issue.1, pp.106-130, 2004.
DOI : 10.1016/j.jcp.2004.01.004

M. Ainsworth, P. Monk, and W. Muniz, Dispersive and Dissipative Properties of Discontinuous Galerkin Finite Element Methods for the Second-Order Wave Equation, Journal of Scientific Computing, vol.15, issue.2, pp.1-3, 2006.
DOI : 10.1007/978-3-662-04823-8

A. F. Loula, G. B. Alvarez, E. G. Do-carmo, and F. A. Rochinha, A discontinuous finite element method at element level for Helmholtz equation, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.4-6, pp.196-867, 2007.
DOI : 10.1016/j.cma.2006.07.008

R. Hiptmair, A. Moiala, and I. Perugia, A Survey of Trefftz Methods for the Helmholtz Equation, 2015.
DOI : 10.1080/00036811.2013.821112

B. Pluymers, B. Van-hal, D. Vandepitte, and W. Desmet, Trefftz-Based Methods for Time-Harmonic Acoustics, Archives of Computational Methods in Engineering, vol.9, issue.2, pp.343-381, 2007.
DOI : 10.1142/S0218396X00000121

C. J. Gittelson, R. Hiptmair, and I. Perugia, -version, ESAIM: Mathematical Modelling and Numerical Analysis, vol.66, issue.2, pp.297-331, 2009.
DOI : 10.1002/nme.1575

R. Hiptmair and I. Perugia, Mixed plane wave DG methods Domain decomposition methods in science and engineering XVIII, Lect. Notes Comput. Sci. Eng, 2008.

R. Hiptmair, A. Moiola, and I. Perugia, Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes, Applied Numerical Mathematics, vol.79, pp.79-91, 2014.
DOI : 10.1016/j.apnum.2012.12.004

B. Després, Sur une formulation variationnelle ultra-faible, Comptes Rendus de l'Académie des Sciences Série I, pp.318-939, 1994.

O. Cessenat and B. Després, Application of an Ultra Weak Variational Formulation of Elliptic PDEs to the Two-Dimensional Helmholtz Problem, SIAM Journal on Numerical Analysis, vol.35, issue.1, pp.255-299, 1998.
DOI : 10.1137/S0036142995285873

G. Gabard, Discontinuous Galerkin methods with plane waves for time-harmonic problems, Journal of Computational Physics, vol.225, issue.2, pp.1961-1984, 2007.
DOI : 10.1016/j.jcp.2007.02.030

A. Buffa and P. Monk, Error estimates for the Ultra Weak Variational Formulation of the Helmholtz equation, ESAIM: Mathematical Modelling and Numerical Analysis, vol.66, issue.6, pp.925-940, 2008.
DOI : 10.1002/nme.1575

B. Cockburn, J. Gopalakrishnan, and R. Lazarov, Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems, SIAM Journal on Numerical Analysis, vol.47, issue.2, pp.1319-1365, 2009.
DOI : 10.1137/070706616

G. Giorgiani, S. Fernández-méndez, and A. Huerta, -adaptivity for wave propagation problems, International Journal for Numerical Methods in Fluids, vol.13, issue.4, pp.1244-1262, 2013.
DOI : 10.1137/1.9780898718027
URL : http://upcommons.upc.edu/bitstream/2117/78723/1/2013-IJNMF-GFH-blanc.pdf

N. C. Nguyen, J. Peraire, F. Reitich, and B. Cockburn, A phase-based hybridizable discontinuous Galerkin method for the numerical solution of the Helmholtz equation, Journal of Computational Physics, vol.290, pp.318-335, 2015.
DOI : 10.1016/j.jcp.2015.02.002

M. Amara, H. Calandra, R. Dejllouli, and M. Grigoroscuta-strugaru, A stable discontinuous Galerkintype method for solving efficiently Helmholtz problems, Computers and Structures, pp.106-107, 2012.
DOI : 10.1016/j.compstruc.2012.05.007

P. Gamallo and R. J. Astley, A comparison of two Trefftz-type methods: the ultraweak variational formulation and the least-squares method, for solving shortwave 2-D Helmholtz problems, International Journal for Numerical Methods in Engineering, vol.38, issue.4, pp.406-432, 2007.
DOI : 10.1002/nme.1948

D. Wang, R. Tezaur, J. Toivanen, and C. Ferhat, Overview of the discontinuous enrichment method, the ultra-weak variational formulation, and the partition of unity method for acoustic scattering in the medium frequency regime and performance comparisons, International Journal for Numerical Methods in Engineering, vol.78, issue.4, pp.403-417, 2012.
DOI : 10.1002/nme.2534

L. Kovalevsky, P. Ladevèze, and H. Riou, The Fourier version of the Variational Theory of Complex Rays for medium-frequency acoustics, Computer Methods in Applied Mechanics and Engineering, vol.225, issue.228, pp.228-142, 2012.
DOI : 10.1016/j.cma.2012.03.009
URL : https://hal.archives-ouvertes.fr/hal-01647876

J. E. Caruthers, J. C. French, and G. K. Raviprakash, GREEN FUNCTION DISCRETIZATION FOR NUMERICAL SOLUTION OF THE HELMHOLTZ EQUATION, Journal of Sound and Vibration, vol.187, issue.4, pp.553-568, 1995.
DOI : 10.1006/jsvi.1995.0544

C. Hofreither, U. Langer, and S. Weisser, Convection-adapted BEM-based FEM, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f??r Angewandte Mathematik und Mechanik, vol.67, issue.7, 2015.
DOI : 10.1016/j.camwa.2014.01.019
URL : http://arxiv.org/pdf/1502.05954

C. Hofreither, A non-standard Finite Element Method using Boundary Integral Operators, 2012.

T. J. Hughes, Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods, Computer Methods in Applied Mechanics and Engineering, vol.127, issue.1-4, pp.387-401, 1995.
DOI : 10.1016/0045-7825(95)00844-9

E. G. Do-carmo, G. B. Alvarez, A. F. Loula, and F. A. Rochinha, A nearly optimal Galerkin projected residual finite element method for Helmholtz problem, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.13-16, pp.1362-1375, 2008.
DOI : 10.1016/j.cma.2007.11.001

D. N. Arnold, An Interior Penalty Finite Element Method with Discontinuous Elements, SIAM Journal on Numerical Analysis, vol.19, issue.4, pp.742-760, 1982.
DOI : 10.1137/0719052

A. Bendali and M. Fares, Boundary Integral Equations Methods in Acoustic Scattering, p.35
DOI : 10.4203/csets.18.1
URL : https://hal.archives-ouvertes.fr/hal-00952225

A. Moiola, R. Hiptmair, and I. Perugia, Plane wave approximation of homogeneous Helmholtz solutions, Zeitschrift f??r angewandte Mathematik und Physik, vol.21, issue.5, pp.809-837, 2011.
DOI : 10.1023/B:ACOM.0000016428.25905.da

E. Spence, An overview of new and old variational formulations for linear elliptic PDEs Unified transform methods for boundary value problems: applications and advances, pp.93-159, 2015.

S. Rienstra, A. Hirschberg, S. W. Rienstra, and &. A. Hirschberg, An introduction to acoustics, 2004.

T. Huttunen, J. P. Kaipio, and P. Monk, The perfectly matched layer for the ultra weak variational formulation of the 3D Helmholtz equation, International Journal for Numerical Methods in Engineering, vol.61, issue.7, pp.61-1072, 2004.
DOI : 10.1002/nme.1105

L. D. Landau and E. M. Lifschitz, Fluid Mechanics 2nd edition, reprinted with corrections, of Landau and Lifschitz: course of theoretical physics, 1987.

J. Nédélec, Acoustic and Electromagnetic Equations: Integral Representations for Harmonic Problems, 2001.

C. H. Wilcox, Scattering theory for the d'Alembert equation in exterior domains, 1975.
DOI : 10.1007/BFb0070581

J. F. Semblat and J. J. Brioist, EFFICIENCY OF HIGHER ORDER FINITE ELEMENTS FOR THE ANALYSIS OF SEISMIC WAVE PROPAGATION, Journal of Sound and Vibration, vol.231, issue.2, pp.460-467, 2000.
DOI : 10.1006/jsvi.1999.2636
URL : https://hal.archives-ouvertes.fr/hal-00355579

W. Mclean, Strongly Elliptic Systems and Boundary Integral Equations, 2000.

D. N. Arnold, F. Brezzi, B. Cockburn, and L. D. Marini, Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems, SIAM Journal on Numerical Analysis, vol.39, issue.5, pp.1749-1779, 2002.
DOI : 10.1137/S0036142901384162

K. Zhao, M. N. Vouvakis, and J. Lee, Solving electromagnetic problems using a novel symmetric FEM-BEM approach, IEEE Transactions on Magnetics, vol.42, issue.4, pp.583-586, 2006.
DOI : 10.1109/TMAG.2006.872489

E. Burman, A. Ern, I. Mozolevski, and B. Stamm, The symmetric discontinuous Galerkin method does not need stabilization in 1D for polynomial orders, Comptes Rendus Mathematique, vol.345, issue.10, pp.599-602, 2007.
DOI : 10.1016/j.crma.2007.10.028
URL : https://hal.archives-ouvertes.fr/hal-01090911

J. S. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin Methods, Algorithms, Analysis, and Applications Texts in Applied Mathematics, vol.54, 2008.
DOI : 10.1007/978-0-387-72067-8
URL : https://link.springer.com/content/pdf/bfm%3A978-0-387-72067-8%2F1.pdf

O. Cessenat, Application d'une nouvelle formulation variationnelle auxéquationsauxéquations d'ondes harmoniques .probì emes d'Helmholtz 2D et de Maxwell 3D, 1996.

P. G. Ciarlet, The Finite Element Method for Elliptic Problems, 1978.

J. Jin, The Finite Element Method in Electromagnetics, 2002.

R. Cools and A. Haegemans, Algorithm 824, ACM Transactions on Mathematical Software, vol.29, issue.3, pp.287-296, 2003.
DOI : 10.1145/838250.838253

T. Huttunen, P. Gamallo, and R. J. Astley, Comparison of two wave element methods for the Helmholtz problem, Communications in Numerical Methods in Engineering, vol.194, issue.2, pp.35-52, 2009.
DOI : 10.1002/cnm.1102

M. J. Gander, F. Magoules, and F. Nataf, Optimized Schwarz Methods without Overlap for the Helmholtz Equation, SIAM Journal on Scientific Computing, vol.24, issue.1, pp.38-60, 2002.
DOI : 10.1137/S1064827501387012
URL : https://hal.archives-ouvertes.fr/hal-00624495

Y. Efendiev and T. Y. Hou, Multiscale Finite Element Methods, of Surveys and Tutorials in the Applied Mathematical Sciences, 2009.

C. Gittelson and R. Hiptmair, Dispersion analysis of plane wave discontinuous Galerkin methods, International Journal for Numerical Methods in Engineering, vol.42, issue.2, pp.313-323, 2014.
DOI : 10.1137/S0036142903423460