We prove the convergence of a spectral discretization of the Vlasov--Poisson system. The velocity term of the Vlasov equation is discretized using either Hermite functions on the infinite domain or Legendre polynomials on a bounded domain. The spatial term of the Vlasov and Poisson equations is discretized using periodic Fourier expansions. Boundary conditions are treated in weak form through a penalty type term that can be applied also in the Hermite case. As a matter of fact, stability properties of the approximated scheme descend from this added term. The convergence analysis is carried out in detail for the 1D-1V case, but results can be generalized to multidimensional domains, obtained as Cartesian product, in both space and velocity. The error estimates show the spectral convergence under suitable regularity assumptions on the exact solution.

Convergence of spectral discretizations of the Vlasov-Poisson system / Manzini, Gianmarco; Funaro, Daniele; Delzanno, Gian Luca. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - 55:5(2017), pp. 2312-2335. [10.1137/16M1076848]

### Convergence of spectral discretizations of the Vlasov-Poisson system

#### Abstract

We prove the convergence of a spectral discretization of the Vlasov--Poisson system. The velocity term of the Vlasov equation is discretized using either Hermite functions on the infinite domain or Legendre polynomials on a bounded domain. The spatial term of the Vlasov and Poisson equations is discretized using periodic Fourier expansions. Boundary conditions are treated in weak form through a penalty type term that can be applied also in the Hermite case. As a matter of fact, stability properties of the approximated scheme descend from this added term. The convergence analysis is carried out in detail for the 1D-1V case, but results can be generalized to multidimensional domains, obtained as Cartesian product, in both space and velocity. The error estimates show the spectral convergence under suitable regularity assumptions on the exact solution.
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2017
55
5
2312
2335
Convergence of spectral discretizations of the Vlasov-Poisson system / Manzini, Gianmarco; Funaro, Daniele; Delzanno, Gian Luca. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - 55:5(2017), pp. 2312-2335. [10.1137/16M1076848]
Manzini, Gianmarco; Funaro, Daniele; Delzanno, Gian Luca
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11380/1150221`
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