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

Authors
Filbet, F
Citation
F. Filbet, Convergence of a finite volume scheme for the Vlasov-Poisson system, CR AC S I, 330(11), 2000, pp. 979-984
Citations number
10
Categorie Soggetti
Mathematics
Journal title
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE
ISSN journal
07644442 → ACNP
Volume
330
Issue
11
Year of publication
2000
Pages
979 - 984
Database
ISI
SICI code
0764-4442(20000601)330:11<979:COAFVS>2.0.ZU;2-W
Abstract
We propose a finite volume scheme to discretize the one-dimensional Vlasov- Poisson system, we prove that, if the initial data is bounded, continuous, and has its first moment bounded, then the numerical approximation weakly c onverges to the solution of the system. Moreover if the initial data belong s to BV, the convergence is strong in C-0([0,T]; L-loc(1)). (C) 2000 Academ ie des sciences/Editions scientifiques et medicales Elsevier SAS.