@article{AIHPC_2003__20_5_731_0, author = {Horsin, T. and Mischler, S. and Vasseur, A.}, title = {On the convergence of numerical schemes for the {Boltzmann} equation}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {731--758}, publisher = {Elsevier}, volume = {20}, number = {5}, year = {2003}, doi = {10.1016/S0294-1449(02)00029-X}, mrnumber = {1995500}, zbl = {1038.82082}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/S0294-1449(02)00029-X/} }
TY - JOUR AU - Horsin, T. AU - Mischler, S. AU - Vasseur, A. TI - On the convergence of numerical schemes for the Boltzmann equation JO - Annales de l'I.H.P. Analyse non linéaire PY - 2003 SP - 731 EP - 758 VL - 20 IS - 5 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S0294-1449(02)00029-X/ DO - 10.1016/S0294-1449(02)00029-X LA - en ID - AIHPC_2003__20_5_731_0 ER -
%0 Journal Article %A Horsin, T. %A Mischler, S. %A Vasseur, A. %T On the convergence of numerical schemes for the Boltzmann equation %J Annales de l'I.H.P. Analyse non linéaire %D 2003 %P 731-758 %V 20 %N 5 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S0294-1449(02)00029-X/ %R 10.1016/S0294-1449(02)00029-X %G en %F AIHPC_2003__20_5_731_0
Horsin, T.; Mischler, S.; Vasseur, A. On the convergence of numerical schemes for the Boltzmann equation. Annales de l'I.H.P. Analyse non linéaire, Volume 20 (2003) no. 5, pp. 731-758. doi : 10.1016/S0294-1449(02)00029-X. http://archive.numdam.org/articles/10.1016/S0294-1449(02)00029-X/
[1] Spaces of functions with differential-difference characteristics and the smoothness of solutions of the transport equation, Dokl. Akad. Nauk SSSR 276 (6) (1984) 1289-1293. | MR | Zbl
,[2] Averaging lemmas without time Fourier transform and application to discretized kinetic equation, Proc. Roy. Soc. Edinburgh Sect. A 129 (1) (1999) 19-36. | MR | Zbl
, ,[3] The Boltzmann Equation and its Application, Springer-Verlag, Berlin, 1988. | MR
,[4] About the splitting algorithm for Boltzmann and B.G.K. equations, Math. Mod. Meth. Appl. Sci. 6 (8) (1996) 1079-1101. | MR | Zbl
, ,[5] On the Cauchy problem for Boltzmann equations: global existence and weak stability, Ann. Math. 130 (1989) 321-366. | MR | Zbl
, ,[6] Global weak solutions of Vlasov-Maxwell systems, Comm. Pure Appl. Math. 42 (1989) 729-757. | MR | Zbl
, ,[7] Global solutions of Boltzmann equation and the entropy inequality, Arch. Rat. Mech. Anal. 114 (1991) 47-55. | MR | Zbl
, ,[8] Lp regularity of velocity averages, Ann. Inst. H. Poincaré Anal. Non Linéaire 8 (1991) 271-287. | Numdam | MR | Zbl
, , ,[9] Relaxation schemes for nonlinear kinetic equations, SIAM J. Numer. Anal. 34 (6) (1997) 2168-2194. | MR | Zbl
, , ,[10] Investigation of the motion of discrete-velocity gases, in: , , (Eds.), Rarefied Gas Dynamics: Theoretical and Computational Techniques, Progress in Astronautics and Aeronautics, 118, AIAA, Washington, DC, 1989.
, , ,[11] Regularity of the moments of the solution of a transport equation, J. Funct. Anal. 76 (1988) 110-125. | MR | Zbl
, , , ,[12] Un résultat de compacité pour l'équation de transport et application au calcul de la valeur propre principale d'un opérateur de transport, C. R. Acad. Sci. 301 (1985) 341-344. | MR | Zbl
, , ,[13] Régularité optimale des moyennes en vitesses, Note C. R. Acad. Sci. Paris, Série I 320 (1995) 911-915. | MR | Zbl
,[14] Régularité optimale des moyennes en vitesses II, C. R. Acad. Sci. Paris, Série I 326 (1998) 945-948. | MR | Zbl
,[15] Une méthode déterministe pour la résolution de l'équation de Boltzmann inhomogène, C. R. Acad. Sci. Paris 314 (1992) 483-487. | MR | Zbl
, , ,[16] Approximation simultanée de réels par des nombres rationnels et noyau de collision de l'équation de Boltzmann, C. R. Acad. Sci. Paris, Série I 330 (2000) 857-862. | MR | Zbl
, ,[17] Convergence of discrete velocities schemes for the Boltzmann equation, Arch. Rat. Mech. Anal. 140 (1997) 53-77. | MR | Zbl
,[18] On the homogeneous spatially Boltzmann equation, Annales de l'Institut Henri Poincaré 16 (4) (1999) 467-501. | Numdam | MR | Zbl
, ,[19] Existence, stability, and convergence of solutions of discrete velocity models to the Boltzmann equation, J. Statist. Phys. 91 (1998) 307-326. | MR | Zbl
, ,[20] Consistency result for a discrete-velocity model of the Boltzmann equation, SIAM J. Numer. Anal. 34 (5) (1997) 1865-1883. | MR | Zbl
, , ,[21] V.A. Panferov, A.G. Heintz, A new consistent discrete-velocity model for the Boltzmann equation, Preprint, University of Goteborg, 1999.
[22] A limiting case for velocity averaging, Ann. Sci. Ecole Norm. Sup. (4) 31 (4) (1998) 591-598. | Numdam | MR | Zbl
, ,[23] A direct method for solving the Boltzmann equation, Proc. du Colloque Eromech 287, Discrete Models in Fluid Dynamics, Transport Theory Statis. Phys. (1-3) (1994). | MR | Zbl
, ,[24] J. Schneider, Une méthode déterministe pour la résolution de l'équation de Boltzmann, Thesis, University Paris 6, France, 1993.
[25] Convergence of a semi-discrete kinetic scheme for the system of isentropic gas dynamics with γ=3, Indiana Univ. Math. J. 48 (1999) 347-364. | Zbl
,[26] Time regularity for the system of isentropic gas dynamics with γ=3, Comm. Partial Differential Equations 24 (1999) 1987-1997. | Zbl
,[27] C. Villani, A review of mathematical topics in collisionnal kinetic theory, to appear. | MR | Zbl
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