Convergence of a Finite Volume Scheme for the Vlasov-Poisson System

We propose a finite volume scheme to discretize the one-dimensional Vlasov-Poisson system. We prove that, if the initial data are positive, bounded, continuous, and have their first moment bounded, then the numerical approximation converges to the weak solution of the system for the weak topology of... L∞. Moreover, if the initial data belong to BV, the convergence is strong in C⁰(0, T; L¹_loc). To prove the convergence of the discrete electric field, we obtain an estimation in W^1,∞ (Ω_T). Then we have f_h(t,x,v)→ f(t,x,v) in $L^\infty(Q_T) weak-\star as h\rightarrow0$, $E_h(t,x)\rightarrow E(t, x) in C^0 (\bar\Omega_T) as h\rightarrow 0$, where (E, f) is the unique weak solution of the Vlasov-Poisson system. Ausführliche Beschreibung Beschreibung ausblenden

1. Person:	Filbet, Francis
Quelle:	in SIAM journal on numerical analysis Vol. 39, No. 4 (2002), p. 1146-1169 Weitere Artikel
Format:	Online-Artikel
Sprache:	English
Veröffentlicht:	2002
Beschreibung:	Online-Ressource
Schlagworte:	research-article Finite Volume Schemes Vlasov-Poisson System Convergence
Online Zugang:	Volltext
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Anmerkung:	Copyright: Copyright 2001 Society for Industrial and Applied Mathematics