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ON THE STABILITY OF CONSERVATIVE DISCONTINUOUS GALERKIN/HERMITE SPECTRAL METHODS FOR THE VLASOV-POISSON SYSTEM

Abstract : We study a class of spatial discretizations for the Vlasov-Poisson system written as an hyperbolic system using Hermite polynomials. In particular, we focus on spectral methods and discontinuous Galerkin approximations. To obtain L 2 stability properties, we introduce a new L 2 weighted space, with a time dependent weight. For the Hermite spectral form of the Vlasov-Poisson system, we prove conservation of mass, momentum and total energy, as well as global stability for the weighted L 2 norm. These properties are then discussed for several spatial discretizations. Finally, numerical simulations are performed with the proposed DG/Hermite spectral method to highlight its stability and conservation features.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03259688
Contributor : Marianne Bessemoulin-Chatard <>
Submitted on : Monday, June 14, 2021 - 2:01:14 PM
Last modification on : Saturday, June 19, 2021 - 3:38:43 AM

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  • HAL Id : hal-03259688, version 1
  • ARXIV : 2106.07468

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Marianne Bessemoulin-Chatard, Francis Filbet. ON THE STABILITY OF CONSERVATIVE DISCONTINUOUS GALERKIN/HERMITE SPECTRAL METHODS FOR THE VLASOV-POISSON SYSTEM. 2021. ⟨hal-03259688v1⟩

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