Journal
KINETIC AND RELATED MODELS
Volume 4, Issue 4, Pages 955-989Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/krm.2011.4.955
Keywords
Vlasov-Poisson system; discontinuous Galerkin; mixed-finite elements; energy conservation
Categories
Funding
- MEC [MTM2008-03541, HI2008-0173]
- CAM [S0505/ESP-0158]
- AGAUR-Generalitat de Catalunya [MTM2008-06349-C03-03 DGI-MCI, 2009-SGR-345]
- NSF [DMS-0809086]
- DOE [DE-FG02-08ER25863]
- Brown University
- IMATI
- ICREA Funding Source: Custom
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We construct a new family of semi-discrete numerical schemes for the approximation of the one-dimensional periodic Vlasov-Poisson system. The methods are based on the coupling of discontinuous Galerkin approximation to the Vlasov equation and several finite element (conforming, non-conforming and mixed) approximations for the Poisson problem. We show optimal error estimates for all the proposed methods in the case of smooth compactly supported initial data. The issue of energy conservation is also analyzed for some of the methods.
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