R. Abgrall, R. Loubère, and J. Ovadia, A Lagrangian Discontinuous Galerkin-type method on unstructured meshes to solve hydrodynamics problems, Int. J. Numer. Meth. Fluids, vol.44, pp.645-663, 2004.

F. L. Adessio, J. K. Baumgardner, N. L. Dukowicz, B. A. Johnson, R. M. Kashiwa et al., CAVEAT: a computer code for fluid dynamics problems with large distortion and internal slip, p.905, 1992.

P. Batten, N. Clarke, C. Lambert, and C. , On the Choice of Wavespeeds for the HLLC Riemann Solver, SIAM Journal on Scientific Computing, vol.18, issue.6, pp.1553-1570, 1997.
DOI : 10.1137/S1064827593260140

C. Berthon, B. Dubroca, and A. Sangam, A Local Entropy Minimum Principle for Deriving Entropy Preserving Schemes, SIAM Journal on Numerical Analysis, vol.50, issue.2, pp.468-491, 2012.
DOI : 10.1137/100814445
URL : https://hal.archives-ouvertes.fr/hal-01280691

B. Boutin, E. Deriaz, P. Hoch, and P. Navaro, Extension of ALE methodology to unstructured conical meshes, ESAIM: Proceedings, pp.31-55, 2011.
DOI : 10.1051/proc/2011011
URL : https://hal.archives-ouvertes.fr/hal-00777271

G. Carré, S. Delpino, B. Després, 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.5160-5183, 2009.
DOI : 10.1016/j.jcp.2009.04.015

J. Cheng and C. Shu, A high order ENO conservative Lagrangian type scheme for the compressible Euler equations, Journal of Computational Physics, vol.227, issue.2, pp.1567-1596, 2007.
DOI : 10.1016/j.jcp.2007.09.017

J. Cheng and C. Shu, A third-order conservative Lagrangian type scheme on curvilinear meshes for the compressible Euler equations, Commun. Comput. Phys, vol.4, pp.1008-1024, 2008.

J. Cheng and C. Shu, Positivity-preserving Lagrangian scheme for multi-material compressible flow, Journal of Computational Physics, vol.257, pp.143-168, 2014.
DOI : 10.1016/j.jcp.2013.09.047

J. Cheng and C. Shu, Second order symmetry-preserving conservative Lagrangian scheme for compressible Euler equations in two-dimensional cylindrical coordinates, Journal of Computational Physics, vol.272, pp.245-265, 2014.
DOI : 10.1016/j.jcp.2014.04.031

B. Cockburn, S. Lin, and C. Shu, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One-dimensional systems, Journal of Computational Physics, vol.84, issue.1, pp.90-113, 1989.
DOI : 10.1016/0021-9991(89)90183-6

B. Cockburn and C. Shu, The Runge???Kutta Discontinuous Galerkin Method for Conservation Laws V, Journal of Computational Physics, vol.141, issue.2, pp.199-224, 1998.
DOI : 10.1006/jcph.1998.5892

B. Després, Lois de Conservation Euleriennes, Lagrangiennes et méthodes numériques, Mathématiques et Applications, 2010.
DOI : 10.1007/978-3-642-11657-5

B. Després and C. Mazeran, 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. Einfeldt, C. Munz, P. L. Roe, and B. J. Sjögreen, On Godunov-type methods near low densities, Journal of Computational Physics, vol.92, issue.2, pp.273-295, 1991.
DOI : 10.1016/0021-9991(91)90211-3

C. Farhat, J. Gerbeau, and A. Rallu, FIVER: A finite volume method based on exact two-phase Riemann problems and sparse grids for multi-material flows with large density jumps, Journal of Computational Physics, vol.231, issue.19
DOI : 10.1016/j.jcp.2012.05.026
URL : https://hal.archives-ouvertes.fr/hal-00703493

G. Gallice, Positive and Entropy Stable Godunov-type Schemes for Gas Dynamics and MHD Equations in Lagrangian or Eulerian Coordinates, Numerische Mathematik, vol.94, issue.4, pp.673-713, 2003.
DOI : 10.1007/s00211-002-0430-0

P. Germain, Mécanique, volume I. Ellipses, 1986.

M. E. Gurtin, E. Fried, and L. Anand, The Mechanics and Thermodynamics of Continua, 2009.
DOI : 10.1017/CBO9780511762956

A. Harten, B. Engquist, S. Osher, and S. Chakravarthy, Uniformly high order accurate essentially non-oscillatory schemes, III, Journal of Computational Physics, vol.71, issue.2, pp.231-303, 1987.
DOI : 10.1016/0021-9991(87)90031-3

R. A. Horn and C. R. Johnson, Matrix analysis, 1985.

G. Jiang and C. Shu, Efficient Implementation of Weighted ENO Schemes, Journal of Computational Physics, vol.126, issue.1, pp.202-228, 1996.
DOI : 10.1006/jcph.1996.0130

J. R. Kamm and F. X. Timmes, On efficient generation of numerically robust Sedov solutions, 2007.

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

B. Van-leer, Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method, Journal of Computational Physics, vol.32, issue.1, pp.101-136, 1979.
DOI : 10.1016/0021-9991(79)90145-1

R. J. Leveque, Finite Volume Methods for Hyperbolic Problems, Cambridge Texts in Applied Mathematics, vol.31, 2002.
DOI : 10.1017/CBO9780511791253

W. Liu, J. Cheng, and C. Shu, High order conservative Lagrangian schemes with Lax???Wendroff type time discretization for the compressible Euler equations, Journal of Computational Physics, vol.228, issue.23, pp.8872-8891, 2009.
DOI : 10.1016/j.jcp.2009.09.001

X. Liu, S. Osher, and T. Chan, Weighted Essentially Non-oscillatory Schemes, Journal of Computational Physics, vol.115, issue.1, pp.200-212, 1994.
DOI : 10.1006/jcph.1994.1187

R. Loubère, Une Méthode Particulaire Lagrangienne de type Galerkin Discontinu Applicationà Applicationà la Mécanique des Fluides et l'Interaction Laser/Plasma, 2002.

P. Maire, Contribution to the numerical modeling of Inertial Confinement Fusion HabilitationàHabilitationà Diriger des Recherches, 2011.

P. Maire, R. Abgrall, J. Breil, R. Loubère, and B. Rebourcet, A nominally second-order cell-centered Lagrangian scheme for simulating elastic???plastic flows on two-dimensional unstructured grids, Journal of Computational Physics, vol.235, pp.626-665, 2013.
DOI : 10.1016/j.jcp.2012.10.017
URL : https://hal.archives-ouvertes.fr/hal-00934989

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-00113542

P. Maire and J. Breil, A second-order cell-centered Lagrangian scheme for two-dimensional compressible flow problems, International Journal for Numerical Methods in Fluids, vol.178, issue.8, pp.1417-1423, 2008.
DOI : 10.1002/fld.1564

P. Maire and B. Nkonga, Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics, Journal of Computational Physics, vol.228, issue.3, pp.799-821, 2009.
DOI : 10.1016/j.jcp.2008.10.012
URL : https://hal.archives-ouvertes.fr/inria-00290717

C. D. Munz, On Godunov-Type Schemes for Lagrangian Gas Dynamics, SIAM Journal on Numerical Analysis, vol.31, issue.1, pp.17-42, 1994.
DOI : 10.1137/0731002

W. F. Noh, Errors for calculations of strong shocks using an artificial viscosity and an artificial heat flux, Journal of Computational Physics, vol.72, issue.1, pp.78-120, 1987.
DOI : 10.1016/0021-9991(87)90074-X

B. Perthame, Second-Order Boltzmann Schemes for Compressible Euler Equations in One and Two Space Dimensions, SIAM Journal on Numerical Analysis, vol.29, issue.1, pp.1-19, 1992.
DOI : 10.1137/0729001

B. Perthame and C. Shu, On positivity preserving finite volume schemes for Euler equations, Numerische Mathematik, vol.73, issue.1, pp.119-130, 1996.
DOI : 10.1007/s002110050187

B. J. Plohr and D. H. Sharp, A conservative Eulerian formulation of the equations for elastic flow, Advances in Applied Mathematics, vol.9, issue.4, pp.481-499, 1988.
DOI : 10.1016/0196-8858(88)90025-5

C. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes, Journal of Computational Physics, vol.77, issue.2, pp.439-471, 1988.
DOI : 10.1016/0021-9991(88)90177-5

F. Vilar, Cell-centered discontinuous Galerkin discretization for two-dimensional Lagrangian hydrodynamics. Computers and Fluids, pp.64-73, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01093675

F. Vilar, P. Maire, and R. Abgrall, Cell-centered discontinuous Galerkin discretizations for two-dimensional scalar conservation laws on unstructured grids and for one-dimensional Lagrangian hydrodynamics, Computers & Fluids, vol.46, issue.1, pp.498-604, 2011.
DOI : 10.1016/j.compfluid.2010.07.018
URL : https://hal.archives-ouvertes.fr/inria-00538165

F. Vilar, P. Maire, and R. Abgrall, A discontinuous Galerkin discretization for solving the two-dimensional gas dynamics equations written under total Lagrangian formulation on general unstructured grids, Journal of Computational Physics, vol.276, pp.188-234, 2014.
DOI : 10.1016/j.jcp.2014.07.030
URL : https://hal.archives-ouvertes.fr/hal-00950782

F. Vilar, C. Shu, and P. Maire, Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: From first-order to high-orders. Part I: The onedimensional case, J. Comp. Phys, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01199605

X. Zhang and C. Shu, On maximum-principle-satisfying high order schemes for scalar conservation laws, Journal of Computational Physics, vol.229, issue.9, pp.3091-3120, 2010.
DOI : 10.1016/j.jcp.2009.12.030

X. Zhang and C. Shu, On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes, Journal of Computational Physics, vol.229, issue.23, pp.8918-8934, 2010.
DOI : 10.1016/j.jcp.2010.08.016

X. Zhang and C. Shu, Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms, Journal of Computational Physics, vol.230, issue.4, pp.1238-1248, 2011.
DOI : 10.1016/j.jcp.2010.10.036

X. Zhang and C. Shu, Positivity-preserving high order finite difference WENO schemes for compressible Euler equations, Journal of Computational Physics, vol.231, issue.5, pp.2245-2258, 2012.
DOI : 10.1016/j.jcp.2011.11.020

X. Zhang, Y. Xia, and C. Shu, Maximum-Principle-Satisfying and Positivity-Preserving High Order Discontinuous Galerkin Schemes for??Conservation Laws on Triangular Meshes, Journal of Scientific Computing, vol.229, issue.1, pp.29-62, 2012.
DOI : 10.1007/s10915-011-9472-8