An Interior Penalty Finite Element Method with Discontinuous Elements, SIAM Journal on Numerical Analysis, vol.19, issue.4, pp.742-760, 1982. ,
DOI : 10.1137/0719052
Functions, SIAM Journal on Numerical Analysis, vol.41, issue.1, pp.306-324, 2003. ,
DOI : 10.1137/S0036142902401311
URL : https://hal.archives-ouvertes.fr/hal-01093487
The mathematical theory of finite element methods, 2008. ,
Asymptotic Preserving Schemes on Distorted Meshes for Friedrichs Systems with Stiff Relaxation: Application to Angular Models in Linear Transport, Journal of Scientific Computing, vol.9, issue.1, pp.371-398, 2015. ,
DOI : 10.1137/090764542
Proof of uniform convergence for a cellcentered AP discretization of the hyperbolic heat equation on general meshes, Mathematics of Computation, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-00956573
Error estimates for the Ultra Weak Variational Formulation of the Helmholtz equation, ESAIM: Mathematical Modelling and Numerical Analysis, vol.66, issue.6, pp.925-940, 2008. ,
DOI : 10.1002/nme.1575
Application of an Ultra Weak Variational Formulation of Elliptic PDEs to the Two-Dimensional Helmholtz Problem, SIAM Journal on Numerical Analysis, vol.35, issue.1, pp.255-299, 1998. ,
DOI : 10.1137/S0036142995285873
Radiative transfer. (International Series of Monographs on Physics) Oxford: Clarendon Press, 1950. ,
Discontinuous Galerkin methods for Friedrichs' systems., in Numerical mathematics and advanced applications, Proceedings of ENUMATH 2005, the 6th European conference on numerical mathematics and advanced applications, pp.79-96, 2005. ,
DOI : 10.1007/978-3-540-34288-5_5
URL : http://cermics.enpc.fr/reports/CERMICS-2005/CERMICS-2005-290.pdf
Functions of several variables Undergraduate Texts in Mathematics, p.10, 1977. ,
Symmetric positive linear differential equations, Communications on Pure and Applied Mathematics, vol.35, issue.3, pp.333-418, 1958. ,
DOI : 10.1002/cpa.3160110306
Discontinuous Galerkin methods with plane waves for the displacement-based acoustic equation, International Journal for Numerical Methods in Engineering, vol.45, issue.3, pp.549-569, 2006. ,
DOI : 10.1007/978-1-4757-3658-8
Discontinuous Galerkin methods with plane waves for time-harmonic problems, Journal of Computational Physics, vol.225, issue.2, pp.1961-1984, 2007. ,
DOI : 10.1016/j.jcp.2007.02.030
-version, ESAIM: Mathematical Modelling and Numerical Analysis, vol.66, issue.2, pp.297-331, 2009. ,
DOI : 10.1002/nme.1575
Computing qualitatively correct approximations of balance laws. Exponential-fit, well-balanced and asymptotic-preserving, 2013. ,
DOI : 10.1007/978-88-470-2892-0
An asymptotic-preserving well-balanced scheme for the hyperbolic heat equations, Comptes Rendus Mathematique, vol.334, issue.4, pp.334-337, 2002. ,
DOI : 10.1016/S1631-073X(02)02257-4
A discretization of the multigroup P N radiative transfer equation on general meshes, Journal of Computational Physics, vol.313, pp.549-582, 2016. ,
DOI : 10.1016/j.jcp.2016.02.058
-Version, SIAM Journal on Numerical Analysis, vol.49, issue.1, pp.264-284, 2011. ,
DOI : 10.1137/090761057
Plane Wave Discontinuous Galerkin Methods: Exponential Convergence of the $$hp$$ h p -Version, Foundations of Computational Mathematics, vol.46, issue.3, pp.637-675, 2016. ,
DOI : 10.1016/S0898-1221(03)90088-5
A Survey of Trefftz Methods for the Helmholtz Equation, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations, pp.237-278, 2016. ,
DOI : 10.1080/00036811.2013.821112
Computational Aspects of the Ultra-Weak Variational Formulation, Journal of Computational Physics, vol.182, issue.1, pp.27-46, 2002. ,
DOI : 10.1006/jcph.2002.7148
Interpolation properties of generalized plane waves, Numerische Mathematik, vol.16, issue.3, pp.683-711, 2015. ,
DOI : 10.1016/0022-247X(66)90160-0
Well-posedness and generalized plane waves simulations of a 2D mode conversion model, Journal of Computational Physics, vol.303, pp.105-124, 2015. ,
DOI : 10.1016/j.jcp.2015.09.033
A generalized plane-wave numerical method for smooth nonconstant coefficients, IMA Journal of Numerical Analysis, vol.34, issue.3, pp.1072-1103, 2014. ,
DOI : 10.1093/imanum/drt030
Asymptotic preserving (AP) schemes for multiscale kinetic and hyperbolic equations: a review, Riv. Mat. Univ. Parma (N.S.), vol.3, pp.177-216, 2012. ,
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
URL : http://www.math.gatech.edu/~jin/PS/Stiff1.ps
A uniformly second order numerical method for the onedimensional discrete-ordinate transport equation and its diffusion limit with interface, Netw. Heterog. Media, pp.35-65, 2009. ,
A priori error analysis of space?time trefftz discontinuous galerkin methods for wave problems, IMA Journal of Numerical Analysis, pp.36-1599, 2016. ,
Diffusion approximations and domain decomposition method of linear transport equations: Asymptotics and numerics, Journal of Computational Physics, vol.292, pp.141-167, 2015. ,
DOI : 10.1016/j.jcp.2015.03.014
Trefftz in translation, Comput. Assist. Mech. Eng. Sci, vol.10, pp.545-563, 2003. ,
The partition of unity finite element method: Basic theory and applications, Computer Methods in Applied Mechanics and Engineering, vol.139, issue.1-4, pp.289-314, 1996. ,
DOI : 10.1016/S0045-7825(96)01087-0
A Discontinuous Galerkin Method for Linear Symmetric Hyperbolic Systems in Inhomogeneous Media, Journal of Scientific Computing, vol.94, issue.1-3, pp.22-23, 2005. ,
DOI : 10.1016/B978-0-12-208350-1.50008-X
A robust SN-DG-approximation for radiation transport in optically thick and diffusive regimes, Journal of Computational Physics, vol.231, issue.4, pp.1947-1962, 2012. ,
DOI : 10.1016/j.jcp.2011.11.017
A Uniform First-Order Method for the Discrete Ordinate Transport Equation with Interfaces in X,Y-Geometry, Journal of Computational Mathematics, vol.27, pp.764-786, 2009. ,
DOI : 10.4208/jcm.2009.09-m2894
Geometric Correction for Diffusive Expansion of Steady Neutron Transport Equation, Communications in Mathematical Physics, vol.252, issue.9, pp.1473-1553, 2015. ,
DOI : 10.1016/j.jde.2011.12.008