Abstract
This paper is devoted to the presentation of a new family of high order numerical schemes in space (first order in time) for the numerical solution of the Euler equations. We restrict the presentation to the 1D case. Full extention to the multi-dimensional case is discussed in [9] with complete discussion of the entropy properties and some numerical simulations. See [8] for an elementary discussion of the entropy inequality.
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References
C. Bernardi and Y. Maday, Approximations spectrales de problèmes aux limites elliptiques. Springer-Verlag, 1992.
O. Cessenat and B. Despres, Application of an ultra weak variational formulation of elliptic PDEs to the 2-dimensional Helmholtz problem. SIAM J. of Numer. Anal., (1998), to appear.
B. Cockburn and C.W. Shu, The Runge-Kutta local projection P 1 discontinuous Galerkin method for scalar conservation laws, M2AN., 25 (1991), 337–361.
B. Cockburn and C.W. Shu, The local discontinuous Galerkin method for time-dependent convection-diffusion systems. Technical Report 9732, ICASE, (1997).
R. Dautray and J.L. Lions, Analyse mathématique et calcul numérique, 9, Evolution: numérique, transport, Masson, Paris, 1987.
B. Despres, Sur une formulation variationnelle de type ultra-faible, Comptes Rendus de l’Académie des Sciences, Série I 318 (1994), 939–944.
B. Despres, Fonctionnelle quadratique et équations intégrales pour les problèmes d’onde harmonique en domaine extérieur, M2AN, 31(3) (1997), 1–57.
B. Despres, Inégalité entropique pour un solveur conservatif du système de la dynamique des gaz en coordonnées de Lagrange, Comptes Rendus de l’Académie des Sciences, PARIS, Série I 324 (1997), 1301–1306.
B. Despres, Inégalités entropiques pour un solveur de type Lagrange ⌿ convection des équations de l’hydrodynamique, Technical Report 2822, CEA, (1997).
B. Despres and S. Jaouen, Solveur entropique d’ordre élevé pour les équations de l’hydrodynamique à deux températures, in preparation.
E. Godlewski and P.A. Raviart, Numerical approximation of hyperbolic systems of conservation laws, Springer-Verlag, 1996.
G. Jiang and C.W. Shu, On a cell entropy inequality for discontinuous Galerkin methods, Math, of Comp., 62 (206) (1994), 531–538.
B. Perthame, Boltzmann type schemes for gas dynamics and the entropy property, Siam J. Numer. Anal., 27 (1990), 1405–1420.
P. L. Roe, Modern numerical methods applicable to stellar pulsation, in The numerical modelling of nonlinear stellar pulsations, Kluwe Academic Publishers, 1990.
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Despres, B. (1999). Entropy Inequality for High Order Discontinuous Galerkin Approximation of Euler Equations. In: Fey, M., Jeltsch, R. (eds) Hyperbolic Problems: Theory, Numerics, Applications. International Series of Numerical Mathematics, vol 129. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8720-5_25
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DOI: https://doi.org/10.1007/978-3-0348-8720-5_25
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9742-6
Online ISBN: 978-3-0348-8720-5
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