T. Alazard, A minicourse on the low Mach number limit. Discrete and Continuous Dynamical Systems series S, pp.365-404, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00535104

G. Browning and H. Kreiss, Problems with Different Time Scales for Nonlinear Partial Differential Equations, SIAM Journal on Applied Mathematics, vol.42, issue.4, pp.704-718, 1982.
DOI : 10.1137/0142049

B. Carreras, H. R. Hicks, and D. K. Lee, Effects of toroidal coupling on the stability of tearing modes, Physics of Fluids, vol.24, issue.1, pp.66-77, 1981.
DOI : 10.1063/1.863247

O. Czarny and G. Huysmans, B??zier surfaces and finite elements for MHD simulations, Journal of Computational Physics, vol.227, issue.16, pp.7423-7445, 2008.
DOI : 10.1016/j.jcp.2008.04.001

M. Constantine and . Dafermos, Non-convex entropies for conservation laws with involutions, Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences, vol.371, p.371, 2005.

B. Després and R. Sart, Reduced resistive MHD in Tokamaks with general density, ESAIM: Mathematical Modelling and Numerical Analysis, vol.46, issue.5, pp.1081-1106
DOI : 10.1051/m2an/2011078

J. F. Drake and T. M. Antonsen, Nonlinear reduced fluid equations for toroidal plasmas, Physics of Fluids, vol.27, issue.4, 1958.
DOI : 10.1063/1.864680

E. Franck, E. Sonnendrücker, M. Hoelzl, and A. Lessig, Energy conservation and numerical stability for the reduced MHD models of the non-linear JOREK code, ESAIM: Mathematical Modelling and Numerical Analysis, vol.49, issue.5, p.2, 2015.
DOI : 10.1051/m2an/2015014

URL : https://hal.archives-ouvertes.fr/hal-01053713

T. A. Gianakon, D. C. Barnes, R. A. Nebel, S. E. Kruger, D. D. Schnack et al., Nonlinear magnetohydrodynamics simulation using high-order finite elements, Journal of Computational Physics, vol.195, p.355, 2004.

J. W. Haverkort, Magnetohydrodynamic Wavesand Instabilities in Rotating Tokamak Plasmas, 2013.

R. Hazeltine and J. Meiss, Shear-Alfv??n dynamics of toroidally confined plasmas, Physics Reports, vol.121, issue.1-2, pp.1-164, 1985.
DOI : 10.1016/0370-1573(85)90083-3

R. Izzo, D. A. Monticello, H. R. Strauss, W. Park, J. Manickam et al., Reduced equations for internal kinks in tokamaks, Physics of Fluids, vol.26, issue.10, pp.3066-3069, 1983.
DOI : 10.1063/1.864030

S. C. Jardin, N. Ferraro, X. Luo, J. Chen, J. Breslau et al., The M3DC1 approach to simulating 3D 2-fluid magnetohydrodynamics in magnetic fusion experiments, Journal of Physics: Conference Series, 2008.

S. Klainerman and A. Majda, Compressible and incompressible fluids, Communications on Pure and Applied Mathematics, vol.33, issue.5, pp.629-653, 1982.
DOI : 10.1002/cpa.3160350503

S. Klainerman and A. Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids, Communications on Pure and Applied Mathematics, vol.71, issue.4, pp.481-524, 1981.
DOI : 10.1002/cpa.3160340405

H. Kreiss, Problems with different time scales for partial differential equations, Communications on Pure and Applied Mathematics, vol.116, issue.3, pp.399-440, 1980.
DOI : 10.1002/cpa.3160330310

S. E. Kruger, C. C. Hegna, and J. D. Callen, Generalized reduced magnetohydrodynamic equations, Physics of Plasmas, vol.5, issue.12, pp.4169-4182, 1998.
DOI : 10.1063/1.873152

URL : http://www.osti.gov/scitech/servlets/purl/314121

D. Peter and . Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, 1973.

A. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, Applied Mathematical Sciences, vol.53
DOI : 10.1007/978-1-4612-1116-7

P. J. Morrison and R. P. Hazeltine, Hamiltonian formulation of reduced magnetohydrodynamics, Physics of Fluids, vol.27, issue.4, pp.886-97, 1984.
DOI : 10.1063/1.864718

P. Ricci, F. Halpern, . Jolliet, . Loizu, . Mosetto et al., Simulation of plasma turbulence in scrape-off layer conditions: the GBS code, simulation results and code validation, Plasma Physics and Controlled Fusion, vol.54, issue.12, p.54124047, 2012.
DOI : 10.1088/0741-3335/54/12/124047

R. Schmalz, Reduced, three-dimensional, nonlinear equations for high-?? plasmas including toroidal effects, Physics Letters A, vol.82, issue.1, pp.14-17, 1981.
DOI : 10.1016/0375-9601(81)90388-1

S. Schochet, Symmetric hyperbolic systems with a large parameter, Communications in Partial Differential Equations, vol.11, issue.15, pp.1627-1651, 1986.
DOI : 10.1007/BF01229377

S. Schochet, Asymptotics for symmetric hyperbolic systems with a large parameter, Journal of Differential Equations, vol.75, issue.1, pp.1-27, 1988.
DOI : 10.1016/0022-0396(88)90126-X

S. Schochet, Fast Singular Limits of Hyperbolic PDEs, Journal of Differential Equations, vol.114, issue.2, pp.476-512, 1994.
DOI : 10.1006/jdeq.1994.1157

A. N. Simakov and P. J. Catto, Drift-ordered fluid equations for modelling collisional edge plasma, Contributions to Plasma Physics, vol.44, issue.13, pp.83-94, 2004.
DOI : 10.1002/ctpp.200410012

H. R. Strauss, Nonlinear, three-dimensional magnetohydrodynamics of noncircular tokamaks, Physics of Fluids, vol.19, issue.1, p.134, 1976.
DOI : 10.1063/1.861310

H. R. Strauss, Dynamics of high ?? tokamaks, Physics of Fluids, vol.20, issue.8, p.1354, 1977.
DOI : 10.1063/1.862018

H. R. Strauss, Reduced MHD in nearly potential magnetic fields, Journal of Plasma Physics, vol.57, issue.1, pp.83-87, 1997.
DOI : 10.1017/S0022377896005296

A. Zeiler, J. F. Drake, and B. Rogers, Nonlinear reduced Braginskii equations with ion thermal dynamics in toroidal plasma, Physics of Plasmas, vol.4, issue.6, 1997.
DOI : 10.1063/1.872368