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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Convergence of classes of high-order semi-Lagrangian schemes for the Vlasov-Poisson system


Authors: Nicolas Besse and Michel Mehrenberger
Journal: Math. Comp. 77 (2008), 93-123
MSC (2000): Primary 65M12
Published electronically: June 18, 2007
MathSciNet review: 2353945
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Abstract: In this paper we present some classes of high-order semi-Lagran- gian schemes for solving the periodic one-dimensional Vlasov-Poisson system in phase-space on uniform grids. We prove that the distribution function $ f(t,x,v)$ and the electric field $ E(t,x)$ converge in the $ L^2$ norm with a rate of

$\displaystyle \mathcal{O}\left(\Delta t^2 +h^{m+1}+ \frac{h^{m+1}}{\Delta t}\right),$

where $ m$ is the degree of the polynomial reconstruction, and $ \Delta t$ and $ h$ are respectively the time and the phase-space discretization parameters.


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Additional Information

Nicolas Besse
Affiliation: Institut de Recherche Mathematique Avancée, Université Louis Pasteur - CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France
Address at time of publication: IECN UMR CNRS 7502 and LPMIA UMR CNRS 7040, Université Henri Poincaré Nancy I, Boulevard des Aiguillettes, B.P. 239 F-54506, Vandoeuvre-lès-Nancy, Cedex, France
Email: besse@iecn.u-nancy.fr

Michel Mehrenberger
Affiliation: Institut de Recherche Mathematique Avancée, Université Louis Pasteur - CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France
Email: mehrenbe@math.u-strasbg.fr

DOI: http://dx.doi.org/10.1090/S0025-5718-07-01912-6
PII: S 0025-5718(07)01912-6
Received by editor(s): March 29, 2005
Received by editor(s) in revised form: May 25, 2005
Published electronically: June 18, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.