S. Agmon, B. F. Jones, J. With, G. W. Batten, and J. , Lectures on elliptic boundary value problems Prepared for publication, Van Nostrand Mathematical Studies, issue.2, 1965.

M. S. Alnaes, A. Logg, and K. Mardal, UFC: a finite element code generation interface, 2012.
DOI : 10.1007/978-3-642-23099-8_16

D. N. Arnold, R. S. Falk, and R. Winther, Finite element exterior calculus, homological techniques, and applications, Acta Numerica, vol.15, pp.1-155, 2006.
DOI : 10.1017/S0962492906210018

D. Boffi, Approximation of eigenvalues in mixed form, Discrete Compactness Property, and application to hp mixed finite elements, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.37-40, pp.3672-3681, 2007.
DOI : 10.1016/j.cma.2006.10.024

D. Boffi, F. Brezzi, and L. Gastaldi, On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form, Mathematics of Computation, vol.69, issue.229, pp.121-140, 2000.
DOI : 10.1090/S0025-5718-99-01072-8

A. Bossavit, Extrusion, contraction: their discretization via Whitney forms, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol.22, issue.3, pp.470-480, 2004.
DOI : 10.1108/03321640310474877

F. Brezzi, L. D. Marini, and E. Süli, DISCONTINUOUS GALERKIN METHODS FOR FIRST-ORDER HYPERBOLIC PROBLEMS, Mathematical Models and Methods in Applied Sciences, vol.14, issue.12, pp.1893-1903, 2004.
DOI : 10.1142/S0218202504003866

P. Castillo, B. Cockburn, I. Perugi, and D. Schötzau, An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems, SIAM Journal on Numerical Analysis, vol.38, issue.5, pp.1676-1706, 2000.
DOI : 10.1137/S0036142900371003

M. Clemens, M. Wilke, and T. Weiland, TD algorithms for transient eddy current problems, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol.20, issue.2, pp.365-379, 2001.
DOI : 10.1108/03321640110383267

A. Ern and J. Guermond, Discontinuous Galerkin Methods for Friedrichs' Systems. I. General theory, SIAM Journal on Numerical Analysis, vol.44, issue.2, pp.753-778, 2006.
DOI : 10.1137/050624133

R. S. Falk and G. R. Richter, Explicit Finite Element Methods for Symmetric Hyperbolic Equations, SIAM Journal on Numerical Analysis, vol.36, issue.3, pp.935-952, 1999.
DOI : 10.1137/S0036142997329463

K. O. Friedrichs, Symmetric positive linear differential equations, Communications on Pure and Applied Mathematics, vol.35, issue.3, pp.333-418, 1958.
DOI : 10.1002/cpa.3160110306

F. G. Fuchs, K. H. Karlsen, S. Mishra, and N. H. Risebro, Stable upwind schemes for the magnetic induction equation, ESAIM: Mathematical Modelling and Numerical Analysis, vol.43, issue.5, pp.2-43, 2009.
DOI : 10.1051/m2an/2009006

F. Henrotte, H. Heumann, E. Lange, and K. Haymeyer, Upwind 3-D Vector Potential Formulation for Electromagnetic Braking Simulations, IEEE Transactions on Magnetics, vol.46, issue.8, pp.2835-2838, 2010.
DOI : 10.1109/TMAG.2010.2043938
URL : https://hal.archives-ouvertes.fr/hal-01108300

H. Heumann, Eulerian and Semi-Lagrangian Methods for Advection-Diffusion of Differential Forms, 2011.

H. Heumann and R. Hiptmair, Eulerian and semi-Lagrangian methods for convection-diffusion for differential forms, Discrete and Continuous Dynamical Systems, vol.29, issue.4, pp.1471-1495, 2011.
DOI : 10.3934/dcds.2011.29.1471
URL : https://hal.archives-ouvertes.fr/hal-01108284

R. Hiptmair, Finite elements in computational electromagnetism. Acta Numer, pp.237-339, 2002.

P. Houston, I. Perugia, A. Schneebeli, and D. Schötzau, Interior penalty method for the indefinite time-harmonic Maxwell equations, Numerische Mathematik, vol.169, issue.3, pp.485-518, 2005.
DOI : 10.1007/s00211-005-0604-7

P. Houston, I. Perugia, A. Schneebeli, and D. Schötzau, Mixed discontinuous Galerkin approximation of the Maxwell operator: The indefinite case, ESAIM: Mathematical Modelling and Numerical Analysis, vol.39, issue.4, pp.2-39, 2005.
DOI : 10.1051/m2an:2005032

P. Houston, I. Perugia, and D. Schötzau, Mixed Discontinuous Galerkin Approximation of the Maxwell Operator, SIAM Journal on Numerical Analysis, vol.42, issue.1, pp.434-459, 2004.
DOI : 10.1137/S003614290241790X

P. Houston, I. Perugia, and D. Schötzau, Mixed Discontinuous Galerkin Approximation of the Maxwell Operator: Non-Stabilized Formulation, Journal of Scientific Computing, vol.169, issue.1-3, pp.315-346, 2005.
DOI : 10.1007/s10915-004-4142-8

P. Houston, C. Schwab, and E. Süli, -Finite Element Methods for Advection-Diffusion-Reaction Problems, SIAM Journal on Numerical Analysis, vol.39, issue.6, pp.2133-2163, 2002.
DOI : 10.1137/S0036142900374111
URL : https://hal.archives-ouvertes.fr/hal-00882219

T. J. Hughes and A. Brooks, A multidimensional upwind scheme with no crosswind diffusion, Finite Element Methods for Convection Dominated Flows, pp.19-35, 1979.

T. J. Hughes, L. P. Franca, and G. M. Hulbert, A new finite element formulation for computational fluid dynamics: VIII. The galerkin/least-squares method for advective-diffusive equations, Computer Methods in Applied Mechanics and Engineering, vol.73, issue.2, pp.73-173, 1989.
DOI : 10.1016/0045-7825(89)90111-4

M. Jensen, Discontinuous Galerkin Methods for Friedrichs Systems with Irregular Solutions, 2005.

M. Jensen, On the Discontinuous Galerkin Method for Friedrichs Systems in Graph Spaces, Lecture Notes in Comput. Sci, vol.3743, pp.94-101, 2006.
DOI : 10.1007/11666806_9

O. A. Karakashian and F. Pascal, A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems, SIAM Journal on Numerical Analysis, vol.41, issue.6, pp.41-2374, 2003.
DOI : 10.1137/S0036142902405217

P. Lasaint and P. Raviart, On a Finite Element Method for Solving the Neutron Transport Equation, Proc. Sympos, pp.89-123, 1974.
DOI : 10.1016/B978-0-12-208350-1.50008-X

A. Logg, G. N. Wells, and J. Hake, DOLFIN: a C++/Python finite element library, Chapt, vol.10, 2012.
DOI : 10.1007/978-3-642-23099-8_10

P. Mullen, A. Mckenzie, D. Pavlov, L. Durant, Y. Tong et al., Discrete Lie Advection of Differential Forms, Foundations of Computational Mathematics, vol.24, issue.1, pp.131-149, 2011.
DOI : 10.1007/s10208-010-9076-y

J. Nédélec, Mixed finite elements in ?3, Numerische Mathematik, vol.12, issue.3, pp.315-341, 1980.
DOI : 10.1007/BF01396415

J. Nédélec, A new family of mixed finite elements in ?3, Numerische Mathematik, vol.39, issue.1, pp.57-81, 1986.
DOI : 10.1007/BF01389668

T. E. Peterson, A Note on the Convergence of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation, SIAM Journal on Numerical Analysis, vol.28, issue.1, pp.133-140, 1991.
DOI : 10.1137/0728006

W. H. Reed and T. R. Hill, Triangular mesh methods for the neutron transport equation, p.NM, 1973.

G. R. Richter, An optimal-order error estimate for the discontinuous Galerkin method, Mathematics of Computation, vol.50, issue.181, pp.75-88, 1988.
DOI : 10.1090/S0025-5718-1988-0917819-3

H. Roos, M. Stynes, and L. Tobiska, Robust numerical methods for singularly perturbed differential equations, Convectiondiffusion-reaction and flow problems, 2008.

G. Zhou, How accurate is the streamline diffusion finite element method?, Mathematics of Computation, vol.66, issue.217, pp.31-44, 1997.
DOI : 10.1090/S0025-5718-97-00788-6