On the stability of conservative discontinuous Galerkin/Hermite spectral methods for the Vlasov-Poisson system

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• Francis Filbet (Université de Toulouse)
• Thursday 26 May 2022, 09:00-10:00
• Seminar Room 1, Newton Institute.

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FKTW05 - Frontiers in numerical analysis of kinetic equations

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.  

This talk is part of the Isaac Newton Institute Seminar Series series.

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