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, Society for Industrial and Applied Mathematics.
History
Submitted: 24 May 2016
Accepted: 25 April 2017
Published online: 26 September 2017
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Los Alamos National Laboratory https://doi.org/10.13039/100008902 : DE-AC52-06NA25396
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