Convergence of a finite volume scheme for the Vlasov-Poisson system

SIAM Journal on Numerical Analysis

Volumn 39, Issue 4, 2002, Pages 1146-1169

  Filbet, Francis ^a  

^a UNIVERSITÉ HENRI POINCARÉ NANCY 1   (France)

Author keywords

Convergence; Finite volume schemes; Vlasov Poisson system

Indexed keywords

EID: 0042922654     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S003614290037321X     Document Type: Article

References (21)

1. J. BATT, The nonlinear Vlasov-Poisson system of partial differential equations in stellar dynamics, Publ. CNER Math. Pures Appl., 5 (1983), pp. 1-30.
2. C. K. BIRDSALL AND A. B. LANGDON, Plasma Physics Via Computer Simulation, McGraw-Hill, New York, 1985.
3. J. P. BORIS AND D. L. BOOK, Solution of continuity equations by the method of flux-corrected transport, J. Comput. Phys., 20 (1976), pp. 397-431.
4. C. Z. CHENG AND G. KNORR, The integration of the Vlasov equation in configuration space, J. Comput. Phys., 22 (1976), pp. 330-351.
5. G.-H. COTTET AND P.-A. RAVIART, Particle methods for the one-dimensional Vlasov-Poisson equations, SIAM J. Numer. Anal., 21 (1984), pp. 52-76.
6. J. COOPER AND A. KLIMAS, Boundary value problems for the Vlasov-Maxwell equation in one dimension, J. Math. Anal. Appl., 75 (1980), pp. 306-329.
7. R. J. DIPERNA AND P. L. LIONS, Solutions globales d'équations du type Vlasov-Poisson, C. R. Acad. Sci. Paris Sér. I Math., 307 (1988), pp. 306-329.
8. E. FIJALKOW, A numerical solution to the Vlasov equation, Comput. Phys. Comm., 116 (1999), pp. 319-328.
9. R. EYMARD, T. GALLOUET, AND R. HERBIN, Finite volume methods, in Handbook of Numerical Analysis, Vol. VII, P. G. Ciarlet and J. L. Lions, eds., North-Holland, Amsterdam, 2000, pp. 713-1020.
10. K. GANGULY AND H. D. VICTORY, JR., On the convergence of particle methods for multidimensional Vlasov-Poisson systems, SIAM J. Numer. Anal., 26 (1989), pp. 249-288.
11. A. J. KLIMAS AND W. M. FARRELL, A splitting algorithm for Vlasov simulation with filamentation filtration, J. Comput. Phys., 110 (1994), pp. 150-163.
12. R. J. LEVEQUE, Numerical Methods for Conservation Laws, Birkhäuser, Basel, 1992.
13. P. MINEAU, Simulation en Physique des Plasmas, Thèse de l'Université d'Orléans, France, 1997.
14. J. SCHAEFFER, Convergence of a difference scheme for the Vlasov-Poisson-Fokker-Planck system in one dimension, SIAM J. Numer. Anal., 35 (1997), pp. 1149-1175.
15. M. SHOUCRI AND G. KNORR, Numerical integration of the Vlasov equation, J. Comput. Phys., 14 (1974), pp. 84-92.
16. E. SONNENDRÜCKER, J. ROCHE, P. BERTRAND, AND A. GHIZZO, The semi-Lagrangian method for the numerical resolution of Vlasov equations, J. Comput. Phys., 149 (1998), pp. 201-220.
17. M.-H. VIGNAL, Convergence of a finite volume scheme for an elliptic-hyperbolic system, RAIRO Model. Math. Anal. Numer., 30 (1996), pp. 841-872.
18. J. P. VILA AND P. VILLEDIEU, Convergence de la méthode des volumes finis pour les systèmes de Friedrichs, C. R. Acad. Sci. Paris Ser. I Math., 325 (1997), pp. 671-676.
19. S. WOLLMAN AND E. OZIZMIR, Numerical approximation of the one-dimensional Vlasov-Poisson system with periodic boundary conditions, SIAM J. Numer. Anal., 33 (1996), pp. 1377-1409.
20. S. WOLLMAN, On the approximation of the Vlasov-Poisson system by particle methods, SIAM J. Numer. Anal., 37 (2000), pp. 1369-1398.
21. Y. ZHENG AND A. MAJDA, Existence of global weak solutions to one-component Vlasov-Poisson and Fokker-Planck-Poisson systems in one space dimension with measures as initial data, Comm. Pure Appl. Math., 47 (1994), pp. 1365-1401.