N. Albin, O. P. Bruno, T. Y. Cheung, and R. O. Cleveland, Fourier continuation methods for high-fidelity simulation of nonlinear acoustic 18 beams, J. Acoust. Soc. Am, vol.132, issue.1
DOI : 10.1121/1.4742722

URL : http://krex.k-state.edu/dspace/bitstream/2097/14990/1/Fourier%20continuation%20-%20publisher%27s%20PDF.pdf

M. A. Averkiou and R. O. Cleveland, Modeling of an electrohydraulic lithotripter with the KZK equation, The Journal of the Acoustical Society of America, vol.106, issue.1, pp.20-102, 1999.
DOI : 10.1121/1.427039

G. E. Barter and D. L. , Shock capturing with PDE-based artificial viscosity for DGFEM: Part I. Formulation, Journal of Computational Physics, vol.229, issue.5, pp.221810-1827
DOI : 10.1016/j.jcp.2009.11.010

URL : http://raphael.mit.edu/darmofalpubs/Barter_JCP.pdf

F. Bassi and S. Rebay, A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible 24

A. Bonito, J. Guermond, and B. Popov, Stability Analysis of Explicit Entropy Viscosity Methods for Non-Linear Scalar Conservation 29
DOI : 10.1090/s0025-5718-2013-02771-8

URL : http://www.math.tamu.edu/%7Eguermond/PUBLICATIONS/bonito_guermond_popov_math-comp_2014.pdf

O. Bou-matar, P. Guerder, Y. Li, B. Vandewoestyne, and K. Van-den-abeele, A nodal discontinuous Galerkin finite element method for nonlinear elastic wave propagation, The Journal of the Acoustical Society of America, vol.131, issue.5, pp.3650-63
DOI : 10.1121/1.3693654

URL : https://hal.archives-ouvertes.fr/hal-00787024

A. N. Brooks and T. J. Hughes, Streamline Upwind/Petrov-Galerkin Formulations For Convection Dominated Flows With Particular 33
DOI : 10.1016/0045-7825(82)90071-8

]. A. Burbeau, P. Sagaut, C. Bruneau, M. S. Canney, V. A. Khokhlova et al., A Problem-Independent Limiter for High-Order Runge?Kutta Discontinuous Galerkin Methods Shock-induced heating and millisecond boiling in gels 37 and tissue due to high intensity focused ultrasound Christopher. Modeling the Dornier HM3 lithotripter, Emphasis On The Incompressible Navier-Stokes Equations. Comput. Methods Appl. Mech. Eng.13] B. Cockburn and C.-W. Shu. TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II, pp.199-259, 1982.

G. Framework, . Math, . Comput-]-b, C. Cockburn, B. Shu et al., The Runge ? Kutta Discontinuous Galerkin Method for Conservation Laws V The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems, J. Comput. Phys, vol.52, issue.141, pp.411-435, 1989.

B. Anal, S. Cockburn, C. Lin, . B. Shu, S. Cockburn et al., TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation 48 laws III: One-dimensional systems The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws 50 IV: The multidimensional case On the equations of nonlinear acoustics A quasi-analytical shock solution for general nonlinear progressive waves Discontinuous Galerkin methods with plane waves for the displacement-based acoustic equation Discontinuous Galerkin methods with plane waves for time-harmonic problems Entropy viscosity method for nonlinear conservation laws, 30] R. Hartmann. Adaptive discontinuous Galerkin methods with shock-capturing for the compressible Navier?Stokes equations, pp.2440-246390, 1990.

R. Hartmann and P. Houston, Adaptive Discontinuous Galerkin Finite Element Methods for the Compressible Euler Equations, Journal of Computational Physics, vol.183, issue.2, pp.9-101131, 2006.
DOI : 10.1006/jcph.2002.7206

W. D. Phys, R. C. Hayes, H. E. Haefeli, M. Kulsrud, O. Henneton et al., Sonic Boom Propagation In A Stratified Atmosphere, With Computer Program. (NASA 22 CR-1299), 1969 Numerical Simulation of Sonic Boom from Hypersonic Meteoroids Filtering in Legendre spectral methods, AIAA Journal Math. Comput, vol.183, issue.77263, pp.508-532, 2008.

J. S. Hesthaven, T. J. Warburton-]-t, M. Hughes, and . Mallet, Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications. Springer Science & 28 Business Media A New Finite Element Formulation For Computational Fluid Dynamics: III. The Generalized Streamline 30, 2007.
DOI : 10.1007/978-0-387-72067-8

]. T. Operator-for-multidimensional-advective-diffusive-systems, M. Hughes, and . Mallet, A New Finite Element Formulation For Computational Fluid Dynamics: IV. A Discontinuity-Capturing 32, Comput. Methods Appl. Mech. Eng, vol.58, pp.305-328, 1986.

]. T. Operator-for-multidimensional-advective-diffusive-systems, L. P. Hughes, M. Franca, and . Mallet, A New Finite Element Formulation For Computational Fluid Dynamics: I. Symmetric Forms 34, Comput. Methods Appl. Mech. Eng, vol.5838, pp.329-336, 1986.

]. T. Hughes, M. Mallet, and A. Mizukami, A new finite element formulation for computational fluid dynamics: I. Symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics, Computer Methods in Applied Mechanics and Engineering, vol.54, issue.2, pp.223-234, 1986.
DOI : 10.1016/0045-7825(86)90127-1

M. Comput, . Appl, . Mech, A. Eng, W. Jameson et al., Numerical solutions of the euler equations by finite volume methods using runge-kutta time-stepping 39 schemes AIAA paper, 1259 Local error analysis for approximate solutions of hyperbolic conservation laws A Smoothness Indicator for Adaptive Algorithms for Hyperbolic Systems, 43] A. Klöckner, T. Warburton, and J.S. Hesthaven. Viscous Shock Capturing in a Time-Explicit Discontinuous Galerkin Method. Math. Model, pp.341-355, 1981.

N. Phenom, D. A. Kopriva, A. Kurganov, Y. Liu, V. P. Kuznetsov et al., Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers Springer Science 47 & Business Media New adaptive artificial viscosity method for hyperbolic systems of conservation laws Equation of nonlinear acoustics Fluid mechanics On a finite element method for solving the neutron transport equation Numerical simulation of transit-time ultrasonic flowmeters by a direct approach, Math. Asp. finite Elem. Partial Differ. 53 equations IEEE Transac- 56 tions on Ultrasonics, Ferroelectrics, and Frequency Control Maday, S. M. O. Kaber, and E. Tadmor. Legendre Pseudospectral Viscosity Method for Nonlinear Conservation Laws. SIAM J. Numer, pp.1-27, 1971.

D. J. Anal, K. J. Maglieri, and . Plotkin, Sonic boom Aeroacoustics Flight Veh The Fourier Method for Nonsmooth Initial Data, Theory Pract. Noise Sources Math. Comput, vol.30, issue.32144, pp.321-342519, 1978.

A. Mcalpine and M. J. Fisher, On the prediction of ???buzz-saw??? noise in acoustically lined aero-engine inlet ducts, Journal of Sound and Vibration, vol.265, issue.1, pp.62-63, 2003.
DOI : 10.1016/S0022-460X(02)01446-3

]. A. Meister, S. Ortleb, . Th, and . Sonar, Application of spectral filtering to discontinuous Galerkin methods on triangulations, Numerical Methods for Partial Differential Equations, vol.29, issue.6, p.65
DOI : 10.1137/040614189