On the convergence of numerical schemes for the Boltzmann equation
T. Horsin; S. Mischler; A. Vasseur
Annales de l'I.H.P. Analyse non linéaire (2003)
- Volume: 20, Issue: 5, page 731-758
- ISSN: 0294-1449
Access Full Article
topHow to cite
topHorsin, T., Mischler, S., and Vasseur, A.. "On the convergence of numerical schemes for the Boltzmann equation." Annales de l'I.H.P. Analyse non linéaire 20.5 (2003): 731-758. <http://eudml.org/doc/78595>.
@article{Horsin2003,
author = {Horsin, T., Mischler, S., Vasseur, A.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {explicit discretization schemes; Maxwellian bounds; time-discrete averaging lemma},
language = {eng},
number = {5},
pages = {731-758},
publisher = {Elsevier},
title = {On the convergence of numerical schemes for the Boltzmann equation},
url = {http://eudml.org/doc/78595},
volume = {20},
year = {2003},
}
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
PB - Elsevier
VL - 20
IS - 5
SP - 731
EP - 758
LA - eng
KW - explicit discretization schemes; Maxwellian bounds; time-discrete averaging lemma
UR - http://eudml.org/doc/78595
ER -
References
top- [1] Agoshkov V.I., Spaces of functions with differential-difference characteristics and the smoothness of solutions of the transport equation, Dokl. Akad. Nauk SSSR276 (6) (1984) 1289-1293. Zbl0599.35009MR753365
- [2] Bouchut F., Desvillettes L., Averaging lemmas without time Fourier transform and application to discretized kinetic equation, Proc. Roy. Soc. Edinburgh Sect. A129 (1) (1999) 19-36. Zbl0933.35159MR1669221
- [3] Cercignani C., The Boltzmann Equation and its Application, Springer-Verlag, Berlin, 1988. Zbl0646.76001MR1313028
- [4] Desvillettes L., Mischler S., About the splitting algorithm for Boltzmann and B.G.K. equations, Math. Mod. Meth. Appl. Sci.6 (8) (1996) 1079-1101. Zbl0876.35088MR1428146
- [5] DiPerna R.J., Lions P.-L., On the Cauchy problem for Boltzmann equations: global existence and weak stability, Ann. Math.130 (1989) 321-366. Zbl0698.45010MR1014927
- [6] DiPerna R.J., Lions P.-L., Global weak solutions of Vlasov–Maxwell systems, Comm. Pure Appl. Math.42 (1989) 729-757. Zbl0698.35128MR1003433
- [7] DiPerna R.J., Lions P.-L., Global solutions of Boltzmann equation and the entropy inequality, Arch. Rat. Mech. Anal.114 (1991) 47-55. Zbl0724.45011MR1088276
- [8] DiPerna R.J., Lions P.-L., Meyer Y., Lp regularity of velocity averages, Ann. Inst. H. Poincaré Anal. Non Linéaire8 (1991) 271-287. Zbl0763.35014MR1127927
- [9] Gabetta E., Pareschi L., Toscani G., Relaxation schemes for nonlinear kinetic equations, SIAM J. Numer. Anal.34 (6) (1997) 2168-2194. Zbl0897.76071MR1480374
- [10] Goldstein D., Sturtevant B., Broadwell J.E., Investigation of the motion of discrete-velocity gases, in: Muntz E.P., Weaver D.P., Campbell D.H. (Eds.), Rarefied Gas Dynamics: Theoretical and Computational Techniques, Progress in Astronautics and Aeronautics, 118, AIAA, Washington, DC, 1989.
- [11] Golse F., Lions P.-L., Perthame B., Sentis R., Regularity of the moments of the solution of a transport equation, J. Funct. Anal.76 (1988) 110-125. Zbl0652.47031MR923047
- [12] Golse F., Perthame B., Sentis R., 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. Zbl0591.45007MR808622
- [13] Lions P.-L., Régularité optimale des moyennes en vitesses, Note C. R. Acad. Sci. Paris, Série I320 (1995) 911-915. Zbl0827.35110MR1328710
- [14] Lions P.-L., Régularité optimale des moyennes en vitesses II, C. R. Acad. Sci. Paris, Série I326 (1998) 945-948. Zbl0922.35135MR1649933
- [15] Martin Y.L., Rogier F., Schneider J., Une méthode déterministe pour la résolution de l'équation de Boltzmann inhomogène, C. R. Acad. Sci. Paris314 (1992) 483-487. Zbl0747.65098MR1154392
- [16] Michel P., Schneider J., Approximation simultanée de réels par des nombres rationnels et noyau de collision de l'équation de Boltzmann, C. R. Acad. Sci. Paris, Série I330 (2000) 857-862. Zbl0960.65145MR1769961
- [17] Mischler S., Convergence of discrete velocities schemes for the Boltzmann equation, Arch. Rat. Mech. Anal.140 (1997) 53-77. Zbl0898.76089MR1482928
- [18] Mischler S., Wennberg B., On the homogeneous spatially Boltzmann equation, Annales de l'Institut Henri Poincaré16 (4) (1999) 467-501. Zbl0946.35075MR1697562
- [19] Palczewski A., Schneider J., Existence, stability, and convergence of solutions of discrete velocity models to the Boltzmann equation, J. Statist. Phys.91 (1998) 307-326. Zbl0918.76048MR1632506
- [20] Palczewski A., Schneider J., Bobylev A., Consistency result for a discrete-velocity model of the Boltzmann equation, SIAM J. Numer. Anal.34 (5) (1997) 1865-1883. Zbl0895.76083MR1472201
- [21] V.A. Panferov, A.G. Heintz, A new consistent discrete-velocity model for the Boltzmann equation, Preprint, University of Goteborg, 1999. Zbl0997.82036
- [22] Perthame B., Souganidis P.E., A limiting case for velocity averaging, Ann. Sci. Ecole Norm. Sup. (4)31 (4) (1998) 591-598. Zbl0956.45010MR1634024
- [23] Rogier F., Schneider J., 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). Zbl0811.76050MR1257657
- [24] J. Schneider, Une méthode déterministe pour la résolution de l'équation de Boltzmann, Thesis, University Paris 6, France, 1993.
- [25] Vasseur A., 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. Zbl1020.65054
- [26] Vasseur A., Time regularity for the system of isentropic gas dynamics with γ=3, Comm. Partial Differential Equations24 (1999) 1987-1997. Zbl0940.35169
- [27] C. Villani, A review of mathematical topics in collisionnal kinetic theory, to appear. Zbl1170.82369MR1942465
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.