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| HAL: hal-00442957, version 2 |
| arXiv: 0912.4952 |
| DOI: 10.1007/s00211-010-0351-2 |
| Detailed view |  Export this paper |
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| Numerische Mathematik / Numerical Mathematics 118, 2 (2011) 329-366 |
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| Available versions: | v1 (2009-12-25) | v2 (2010-07-30) |
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| Analysis of a new class of Forward Semi-Lagrangian schemes for the 1D Vlasov-Poisson Equations |
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| Thomas Respaud 1, 2Eric Sonnendrücker 1, 2 |
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| (2011) |
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| 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. |
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| 1: | Institut de Recherche Mathématique Avancée (IRMA) |
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CNRS : UMR7501 – Université de Strasbourg |
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| 2: | CALVI (INRIA Nancy - Grand Est / IECN / LSIIT / IRMA) |
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CNRS : UMR7005 – INRIA – Université de Strasbourg – Université de Lorraine |
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| Subject | : | Mathematics/Numerical Analysis |
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| semi-Lagrangien – schéma numérique – convergence – Vlasov |
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| Attached file list to this document: | ||||||||||
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| hal-00442957, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00442957 | |
| oai:hal.archives-ouvertes.fr:hal-00442957 | |
| From: Eric Sonnendrücker | |
| Submitted on: Friday, 30 July 2010 15:24:06 | |
| Updated on: Wednesday, 22 June 2011 10:45:36 | |
