. [. Bibliographie, T. Aavatsmark, O. Barkve, T. Boe, and . Mannseth, Discretization on non-orthogonal, quadrilateral grids for inhomogeneous, anisotropic media, J. Comput. Phys, vol.127, pp.2-14, 1996.

I. Aavatsmark and G. Eigestad, Numerical convergence of the MPFA O-method and U-method for general quadrilateral grids, International Journal for Numerical Methods in Fluids, vol.6, issue.9-10, pp.939-961, 2006.
DOI : 10.1002/fld.1096

G. Allaire and F. , Golse Transport et diffusion

R. [. Angelas and . Masson, Convergence of the finite volume MPFA O scheme for heterogeneous anisotropic diffusion problems on general meshes, Comptes Rendus Mathematique, vol.346, issue.17-18, pp.1007-1012, 2008.
DOI : 10.1016/j.crma.2008.07.015

R. [. Angelas, R. Eymard, and . Herbin, A nine-point finite volume scheme for the simulation of diffusion in heterogeneous media, Comptes Rendus Mathématiques, vol.347, pp.11-12, 2009.

J. Breil and P. Maire, A cell-centered diffusion scheme on two-dimensional unstructured meshes, Journal of Computational Physics, vol.224, issue.2, pp.785-823, 2007.
DOI : 10.1016/j.jcp.2006.10.025

S. Atzeni and J. Meyer-ter-vehn, The physics of inertial fusion, Oxford Science publications, 2004.
DOI : 10.1093/acprof:oso/9780198562641.001.0001

C. Berthon, C. Buet, J. Coulombel, B. Desprès, J. Dubois et al., Mathematical Models and Numerical Methods for Radiative Transfer

C. Berthon, P. Charrier, and R. Turpault, An HLLC Scheme to Solve The M 1 Model of Radiative Transfer in Two Space Dimensions, Journal of Scientific Computing, vol.94, issue.3???4, pp.347-389, 2007.
DOI : 10.1007/s10915-006-9108-6
URL : https://hal.archives-ouvertes.fr/hal-00293559

C. Berthon, J. Dubois, B. Dubroca, T. Nguyen-bui, and R. Turpault, A free streaming contact preserving scheme for the M 1 model, Advances in Applied Mathematics and Mechanics Adv. Appl. Math. Mech, vol.3, pp.259-285, 2010.

C. Berthon, P. Lefloch, and R. Turpault, Late-time relaxation limits of nonlinear hyperbolic systems. A general framework

C. Berthon, F. Marche, and R. Turpault, An efficient scheme on wet/dry transitions for shallow water equations with friction, Computers & Fluids, vol.48, issue.1, pp.192-201, 2011.
DOI : 10.1016/j.compfluid.2011.04.011
URL : https://hal.archives-ouvertes.fr/hal-00799075

C. Berthon and R. Turpault, Asymptotic preserving HLL schemes, Numerical Methods for Partial Differential Equations, vol.94, issue.6, pp.1396-1422, 2011.
DOI : 10.1002/num.20586

H. [. Bouchut, B. Ounaissa, and . Perthame, Upwinding of the source term at interfaces for Euler equations with high friction, Computers & Mathematics with Applications, vol.53, issue.3-4, pp.3-4361, 2007.
DOI : 10.1016/j.camwa.2006.02.055

F. Bouchut, Nonlinear stability of finite volumes methods for hyperbolic conservation laws and well-balanced schemes for sources Frontiers in mathematics, 2004.

B. Boutin, E. Deriaz, P. Hoch, and P. Navarro, Extention of ALE methodology to unstructured conical meshes, ESAIM : Proceedings, Octobre 2011, pp.31-55

K. [. Brezzi and V. Lipnikov, A FAMILY OF MIMETIC FINITE DIFFERENCE METHODS ON POLYGONAL AND POLYHEDRAL MESHES, Mathematical Models and Methods in Applied Sciences, vol.15, issue.10, pp.1533-1553, 2005.
DOI : 10.1142/S0218202505000832

T. Brunner, Riemann solvers for time-dependant transport based on the maximum entropy and spherical harmonics closures

]. T. Bru02 and . Brunner, Form of approximate radiation transport, 2002.

T. Brunner and J. P. Holloway, Two-dimensional time dependent Riemann solvers for neutron transport, Journal of Computational Physics, vol.210, issue.1, pp.386-399, 2005.
DOI : 10.1016/j.jcp.2005.04.011

C. Buet and S. Cordier, An asymptotic preserving scheme for hydrodynamics radiative transfer models, Numerische Mathematik, vol.325, issue.2, pp.199-221, 2007.
DOI : 10.1007/s00211-007-0094-x

C. Buet, S. Cordier, B. Lucquin-desreux, and S. Mancini, Diffusion Limit of the Lorentz Model: Asymptotic Preserving Schemes, ESAIM: Mathematical Modelling and Numerical Analysis, vol.36, issue.4, pp.631-655, 2002.
DOI : 10.1051/m2an:2002028

C. Buet and B. Després, Asymptotic preserving and positive schemes for radiation hydrodynamics, Journal of Computational Physics, vol.215, issue.2, pp.2-717, 2006.
DOI : 10.1016/j.jcp.2005.11.011

C. Buet, B. Després, and E. Franck, Design of asymptotic preserving schemes for the hyperbolic heat equation on unstructured meshes Numerish Mathematik

]. C. Bdfcras, B. Buet, E. Després, and . Franck, Asymptotic preserving scheme with maximum principle for non linear radiative transfer model on unstructured meshes

]. C. Bdfproc, B. Buet, E. Després, and . Franck, Asymptotic preserving finite volumes discretization for non-linear moment model on unstructured meshes, 2011.

C. Buet and B. Desprès, Asymptotic analysis of fluid models for the coupling of radiation and hydrodynamics, Journal of Quantitative Spectroscopy and Radiative Transfer, vol.85, issue.3-4, pp.385-418, 2004.
DOI : 10.1016/S0022-4073(03)00233-4

G. [. Cargo and . Samba, Resolution of the time dependant P n equations by a godunov scheme having diffusion limit, pp.2-44, 2010.

G. Carré, S. Del-pino, B. Desprès, and E. Labourasse, A cell-centered Lagrangian hydrodynamics scheme on general unstructured meshes in arbitrary dimension, Journal of Computational Physics, vol.228, issue.14, pp.5160-518, 2009.
DOI : 10.1016/j.jcp.2009.04.015

F. [. Chalons, E. Coquel, P. Godlewski, N. Raviart, and . Seguin, GODUNOV-TYPE SCHEMES FOR HYPERBOLIC SYSTEMS WITH PARAMETER-DEPENDENT SOURCE: THE CASE OF EULER SYSTEM WITH FRICTION, Mathematical Models and Methods in Applied Sciences (M3AS), pp.2109-2166, 2010.
DOI : 10.1142/S021820251000488X
URL : https://hal.archives-ouvertes.fr/hal-00401616

A. Chinnayya, A. Leroux, and N. Seguin, A well-balanced numerical scheme for the approximation of the shallow-water equations with topography : the resonance phenomenon, Int. J. Finite Volumes, pp.1-33, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00017378

A. Claisse, B. Després, E. Labourasse, and F. Ledoux, A new exceptional points method with application to cell-centered Lagrangian schemes and curved meshes, Journal of Computational Physics, vol.231, issue.11
DOI : 10.1016/j.jcp.2012.02.017
URL : https://hal.archives-ouvertes.fr/hal-01437591

J. [. Coudì-ere, P. Vila, and . Villedieu, Convergence d'un sch??ma volumes finis explicite en temps pour les syst??mes hyperboliques lin??aires sym??triques en domaines born??s, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.331, issue.1, pp.95-100, 2000.
DOI : 10.1016/S0764-4442(00)00502-4

G. Coppa, Deduction of a symmetric tensor formulation of the PN method for the linear transport equation, Progress in Nuclear Energy, vol.52, issue.8, pp.474-752, 2010.
DOI : 10.1016/j.pnucene.2010.05.005

E. [. Coquel, P. Godlewski, N. Raviart, and . Seguin, An asymptotic preserving scheme for Euler equations with gravity and friction, Finite volumes for complex applications V, pp.8-13, 2008.

M. [. Crouseilles and . Lemou, An asymptotic preserving scheme based on a micro-macro decomposition for Collisional Vlasov equations: diffusion and high-field scaling limits, Kinetic and Related Models, vol.4, issue.2, pp.441-477, 2011.
DOI : 10.3934/krm.2011.4.441
URL : https://hal.archives-ouvertes.fr/hal-00533327

P. Degond, F. Deluzet, A. Sangam, and M. Vignal, An Asymptotic Preserving scheme for the Euler equations in a strong magnetic field, Journal of Computational Physics, vol.228, issue.10, pp.3540-3558, 2009.
DOI : 10.1016/j.jcp.2008.12.040
URL : https://hal.archives-ouvertes.fr/hal-00319630

S. [. Degond, F. Gallego, and . Méhats, An asymptotic preserving scheme for the Schr??dinger equation in the semiclassical limit, Comptes Rendus Mathematique, vol.345, issue.9, pp.531-536, 2007.
DOI : 10.1016/j.crma.2007.10.014

J. [. Degond, M. Liu, and . Vignal, Analysis of an Asymptotic Preserving Scheme for the Euler???Poisson System in the Quasineutral Limit, SIAM Journal on Numerical Analysis, vol.46, issue.3, pp.1298-1322, 2008.
DOI : 10.1137/070690584
URL : https://hal.archives-ouvertes.fr/hal-00635071

]. J. Dem06, Demailly Analyse numérique etéquationsetéquations différentielles, collection Grenobles sciences

B. Després and C. , Lagrangian Gas Dynamics in Two Dimensions and Lagrangian systems, Archive for Rational Mechanics and Analysis, vol.180, issue.3, pp.327-372, 2005.
DOI : 10.1007/s00205-005-0375-4

B. Després and C. , Mazeran Lagrangian gas dynamics in 2D and Lagrangian systems, C. R. Acad. Sci (Paris), vol.331, pp.475-480, 2003.

D. Donatelli and P. , Marcati Convergence of singular limits for multi-D semilinear hyperbolic systems to parabolic systems, Transactions of the American Mathematical Society, vol.356, issue.05, pp.2093-2121, 2004.
DOI : 10.1090/S0002-9947-04-03526-3

J. Droniou, R. Eymard, T. Gallouet, and R. , Herbin A unified approach to mimetic finite difference, hydrid finite volume and mixed finite volume methods, Math. Models Methods Appl

J. Droniou and C. , Le-Potier Construction and convergence study of local-maximum-principe preserving schemes for elliptic equations, SIAM journal on numerical analysis, vol.49, pp.1-2, 2011.

J. [. Dubroca, Feugeas Hiérarchie des modèles aux moments pour le transfert radiatif, C. R
DOI : 10.1016/s0764-4442(00)87499-6

. Acad and . Sci, Paris t.329, serie I, pp.915-920, 1999.

C. Enaux, Analyse mathématique et numérique d'un modèle multifluide multivitesse pour l'interpénétration de fluides miscibles, 2007.

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

J. [. Ern and . Guermond, Discontinuous Galerkin Methods for Friedrichs??? Systems. Part II. Second???order Elliptic PDEs, SIAM Journal on Numerical Analysis, vol.44, issue.6, pp.2363-2388, 2006.
DOI : 10.1137/05063831X

T. [. Eymard, R. Gallouet, and . Herbin, The finite volume method, Handbook for Numerical Analysis, Ph. Ciarlet J.L. Lions eds, pp.715-1022, 2000.

T. [. Eymard, R. Gallouet, and . Herbin, Discretisation of heteregeneous and anisotropic diffusion problem on general noncorforming meshes, IMA J. Num. Anal, 2009.

F. Filbet and S. Jin, A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources, Journal of Computational Physics, vol.229, issue.20, pp.7625-7648, 2010.
DOI : 10.1016/j.jcp.2010.06.017
URL : https://hal.archives-ouvertes.fr/hal-00659668

E. Franck, P. Hoch, G. Samba, and P. Navarro, An asymptotic preserving scheme for P 1 model using classical diffusion schemes on unstructured polygonal meshes, ESAIM : Proceedings, Octobre 2011, pp.56-75

M. Frank, Approximate models for radiative transfer, Bull. Inst. Math. Acad. Sinica (New Series), vol.2, pp.409-432, 2007.

M. Frank, A. Klar, E. W. Larsen, and S. Yasuda, Time-dependent simplified PN approximation to the equations of radiative transfer, Journal of Computational Physics, vol.226, issue.2, pp.2289-2305, 2007.
DOI : 10.1016/j.jcp.2007.07.009

G. Gallice, Solveurs simples positifs et entropiques pour les syst??mes hyperboliques avec terme source, Comptes Rendus Mathematique, vol.334, issue.8, pp.713-716, 2002.
DOI : 10.1016/S1631-073X(02)02307-5

T. Gallouet, J. M. Herard, and N. , Seguin Some approximate Godunov schemes to compute shallow water equations with topography, Comput. and Fluids, vol.323, issue.4 31, pp.479-513, 2003.

E. Godlewski and P. Raviart, Hyperbolic systems of conservation laws
URL : https://hal.archives-ouvertes.fr/hal-00113734

]. L. Gos10 and . Gosse, Asymptotic preserving and well-balanced scheme for the 1D Cattaneo model of chemotaxis movement in both hyperbolic and diffusive regimes, Journal of Mathematical Analysis and Applications, vol.388, issue.2, pp.964-983, 2012.

L. Gosse, Transient radiative transfer in the grey case: Well-balanced and asymptotic-preserving schemes built on Case's elementary solutions, Journal of Quantitative Spectroscopy and Radiative Transfer, vol.112, issue.12, pp.1995-2012, 2011.
DOI : 10.1016/j.jqsrt.2011.04.003

L. Gossegt01-]-l, G. Gosse, and . Toscani, Well-Balanced schemes using elementary solutions for linear models of the Boltzmann equation in one space dimension An asymptotic-preserving well-balanced scheme for the hyperbolic heat equations, C. R. Acad. Sci Paris,Ser. I, vol.334, pp.337-342, 2002.

L. Gosse and G. Toscani, Asymptotic-preserving & well-balanced schemes for radiative transfer and the Rosseland approximation, Numerische Mathematik, vol.9, issue.2, pp.223-250, 2004.
DOI : 10.1007/s00211-004-0533-x

J. Greenberg and A. Y. Leroux, A Well-Balanced Scheme for the Numerical Processing of Source Terms in Hyperbolic Equations, SIAM Journal on Numerical Analysis, vol.33, issue.1, 1996.
DOI : 10.1137/0733001

C. D. Hauck, R. B. Lowrie, and R. Mcclarren, Methods for diffusive relaxation in P n equations , Numerical methods for relaxation systems and balance equations

F. Hermeline, A Finite Volume Method for the Approximation of Diffusion Operators on Distorted Meshes, Journal of Computational Physics, vol.160, issue.2, pp.481-499, 2000.
DOI : 10.1006/jcph.2000.6466

F. Hermeline, Approximation of 2-D and 3-D diffusion operators with variable full tensor coefficiens on arbitrary meshes, Computer Methods in Applied Mechanics and Engineering, vol.196, pp.21-24, 2007.

[. Jin and D. Levermore, The discrete-ordinate method in diffusive regimes, Transport Theory and Statistical Physics, vol.62, issue.5-6, pp.413-439, 1991.
DOI : 10.1016/0021-9991(87)90170-7

[. Jin and D. Levermore, Numerical Schemes for Hyperbolic Conservation Laws with Stiff Relaxation Terms, Journal of Computational Physics, vol.126, issue.2, pp.449-467, 1996.
DOI : 10.1006/jcph.1996.0149

[. Jin and Z. Xin, The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications on Pure and Applied Mathematics, vol.54, issue.3, pp.235-277, 1995.
DOI : 10.1002/cpa.3160480303

]. S. Jin99 and . Jin, Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations, SIAM Journal on Scientific Computing, vol.21, issue.2, pp.441-454, 1999.
DOI : 10.1137/S1064827598334599

S. Jin and B. Yan, A class of asymptotic-preserving schemes for the Fokker???Planck???Landau equation, Journal of Computational Physics, vol.230, issue.17, pp.6420-6437, 2011.
DOI : 10.1016/j.jcp.2011.04.002

]. S. Jin11 and . Jin, Asymptotic preserving (AP) schemes for multiscale kinetic and hyperbolic equations : a review, Lecture Notes for Summer School on « Methods and Models of Kinetic Theory » (M and MKT), 2010.

D. Kershaw, Differencing of the diffusion equation in Lagrangian hydrodynamic codes, Journal of Computational Physics, vol.39, issue.2, pp.375-395, 1981.
DOI : 10.1016/0021-9991(81)90158-3

]. G. Klu08 and . Kluth, Analyse mathématique et numérique de systèmes hyperélastiques et introductioná?A introductionáintroductioná? introductioná?A la plasticité, 2008.

G. Kluth and B. Després, Discretization of hyperelasticity on unstructured mesh with a cell-centered Lagrangian scheme, Journal of Computational Physics, vol.229, issue.24, pp.9092-9118, 2010.
DOI : 10.1016/j.jcp.2010.08.024

Y. Kuznetsov, K. Lipnikov, and M. Shashkov, The mimetic finite difference method on polygonal meshes for diffusion-type problems, Computational Geosciences, vol.88, issue.3/4, pp.301-324
DOI : 10.1007/s10596-004-3771-1

M. Lemou and L. Mieussens, A New Asymptotic Preserving Scheme Based on Micro-Macro Formulation for Linear Kinetic Equations in the Diffusion Limit, SIAM Journal on Scientific Computing, vol.31, issue.1, pp.334-368
DOI : 10.1137/07069479X
URL : https://hal.archives-ouvertes.fr/hal-00348594

M. Lemou, Relaxed micro???macro schemes for kinetic equations, Comptes Rendus Mathematique, vol.348, issue.7-8, pp.455-460, 2010.
DOI : 10.1016/j.crma.2010.02.017
URL : https://hal.archives-ouvertes.fr/hal-00521523

]. C. Lepo09, Le Potier Un schéma linéaire vérifiant le principe du maximum pour des opérateurs de diffusion très anisotropes sur des maillages déformés, Comptes Rendus Mathématique, vol.347, pp.105-110, 2009.

]. C. Lepo09 and A. Le-potier, Mahamane Correction non linéaire et principe du maximum avec des schémas hybrides pour la discrétisation d'opérateurs de diffusion, Comptes Rendus Mathématique, vol.350, pp.101-106, 2012.

J. [. Lipnikov, M. Morel, and . Shashkov, Mimetic finite difference methods for diffusion equations on non-orthogonal non-conformal meshes, Journal of Computational Physics, vol.199, issue.2, pp.589-597, 2004.
DOI : 10.1016/j.jcp.2004.02.016

M. [. Lipnikov, D. Shashkov, Y. Svyatskiy, and . Vassilevski, Monotone finite volume schemes for diffusion euqations on unstructured triangular and shape-regular polygonal meshes, JCP, vol.227, pp.492-512, 2007.

C. Mazeran, Sur la structure mathématique et l'approximation numérique de l'hydrodynamique Lagrangienne bidimensionelle, 2007.

P. Maire, R. Abgrall, J. Breil, and J. Ovadia, A Cell-Centered Lagrangian Scheme for Two-Dimensional Compressible Flow Problems, SIAM Journal on Scientific Computing, vol.29, issue.4, pp.1781-1824, 2007.
DOI : 10.1137/050633019
URL : https://hal.archives-ouvertes.fr/inria-00334022

[. Maire, Contribution to the numerical modeling of inertial confinement fusion, Hdr

]. R. Mch10, C. D. Mcclarren, and . Hauck, Simulating radiative transfer with flitered spherical harmonics, Physics Letters A, vol.374, pp.2290-2296, 2010.

R. Mcclarren, C. D. Hauck, and R. Lowrie, Filtered spherical harmonics methods for transports problems, Proceedings of the 2009 international conference on mathematics and computational methods and reactor physics, 2008.

R. Mcclarren and R. Lowrie, Manufactured solutions for the radiation-hydrodynamics equations, Journal of Quantitative Spectroscopy and Radiative Transfer, vol.109, issue.15, pp.2590-2602, 2008.
DOI : 10.1016/j.jqsrt.2008.06.003

]. R. Mchl10, R. Mcclarren, and . Lowrie, The effects of slope limiting on asymptotic-preserving numerical methods for hyperbolic conservation laws, Journal of Computational Physics, vol.227, pp.9711-9726, 2008.

M. [. Monreal and . Franck, Higher order minimum entropy approximations in radiative transfer

R. Natalini and M. Ribot, Asymptotic High Order Mass-Preserving Schemes for a Hyperbolic Model of Chemotaxis, SIAM Journal on Numerical Analysis, vol.50, issue.2, 2012.
DOI : 10.1137/100803067
URL : https://hal.archives-ouvertes.fr/hal-00765703

L. [. Olson, M. L. Auer, and . Hall, Diffusion, P1, and other approximate forms of radiation transport, Journal of Quantitative Spectroscopy and Radiative Transfer, vol.64, issue.6, 1999.
DOI : 10.1016/S0022-4073(99)00150-8

]. S. Pa08 and . Paul, Etude d'un schéma numérique volumes finis avec bilan des flux aux coins pour l'ALE, Rapport stage M2, 2008.

J. Planchard, Méthode mathématique en neutronique, Eyrolles, 1995.

]. S. Sah11 and . Sahmin, Un schéma aux volumes finis avec matrice signe pour les systèmes non homogènes, Thèse, 2005.

M. Schafer, M. Frank, and C. D. Levermore, Diffusive Corrections to $P_N$ Approximations, Multiscale Modeling & Simulation, vol.9, issue.1, pp.1-28, 2011.
DOI : 10.1137/090764542

Z. Sheng, J. Yue, and G. Yuan, Monotone finite volume schemes of nonequilibrium radiation diffuison equations of distortes meshes SIAM, J. Sci. Comput, vol.31, issue.4, pp.2915-2934

]. E. Tor28, Toro Riemann Solvers and Numerical Methods for Fluid Dynamics : A Practical Introduction, 2008.

]. R. Tur03 and . Turpault, Modélisation, approximation numérique et applications du transfert radiatif en déséquilibre spectral couplé avec l'hydrodynamique, Thèse, 2003.

M. Vohralik, Equivalence between lowest-order mixed finite element and multi-point finite volume methods on simplicial meshes, ESAIM: Mathematical Modelling and Numerical Analysis, vol.40, issue.2, pp.2-367, 2006.
DOI : 10.1051/m2an:2006013
URL : https://hal.archives-ouvertes.fr/hal-00114646