hal-00442957, version 2
Analysis of a new class of Forward Semi-Lagrangian schemes for the 1D Vlasov-Poisson Equations
Numerische Mathematik / Numerical Mathematics 118, 2 (2011) 329-366
Résumé : The Vlasov equation is a kinetic model describing the evolution of charged particles, and is coupled with Poisson's equation, which rules the evolution of the self-consistent electric field. In this paper, we introduce a new class of forward Semi-Lagrangian schemes for the Vlasov-Poisson system based on a Cauchy Kovalevsky (CK) procedure for the numerical solution of the characteristic curves. Exact conservation properties of the first moments of the distribution function for the schemes are derived and a convergence study is performed that applies as well for the CK scheme as for a more classical Verlet scheme. The convergence in L1 norm of the schemes is proved and error estimates are obtained.
- a – Université Louis Pasteur - Strasbourg I
- 1 :
- CNRS : UMR7501 – Université de Strasbourg
- 2 :
- CNRS : UMR7005 – INRIA – Université de Strasbourg – Université de Lorraine
- Domaine : Mathématiques/Analyse numérique
- Mots-clés : semi-Lagrangien – schéma numérique – convergence – Vlasov
- Versions disponibles : v1 (25-12-2009) v2 (30-07-2010)
- hal-00442957, version 2
- http://hal.archives-ouvertes.fr/hal-00442957
- oai:hal.archives-ouvertes.fr:hal-00442957
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- Soumis le : Vendredi 30 Juillet 2010, 15:24:06
- Dernière modification le : Mercredi 22 Juin 2011, 10:45:36
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