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Article Dans Une Revue SIAM Journal on Numerical Analysis Année : 2023

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

Résumé

We prove the convergence of discontinuous Galerkin approximations for the Vlasov-Poisson system written as an hyperbolic system using Hermite polynomials in velocity. To obtain stability properties, we introduce a suitable weighted L 2 space, with a time dependent weight, and first prove global stability for the weighted L 2 norm and propagation of regularity. Then we prove error estimates between the numerical solution and the smooth solution to the Vlasov-Poisson system.
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Dates et versions

hal-03760711 , version 1 (25-08-2022)
hal-03760711 , version 2 (30-01-2023)

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Paternité

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Marianne Bessemoulin-Chatard, Francis Filbet. On the convergence of discontinuous Galerkin/Hermite spectral methods for the Vlasov-Poisson system. SIAM Journal on Numerical Analysis, 2023, 61 (4), pp.1664-1688. ⟨10.1137/22M1518232⟩. ⟨hal-03760711v2⟩
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