Convergence of Galerkin approximation for two-dimensional Vlasov-Poisson equation

  • M. Pulvirenti
  • J. Wick
Original Papers
Received:
Revised:

Abstract

We give explicit estimates on the rate of convergence of the solutions of finite dimensional truncations (by means of Fourier-Hermite expansion) of Vlasov-Poisson equation in a two-dimensional flat torus.

Keywords

Mathematical Method Galerkin Approximation Explicit Estimate Flat Torus Dimensional Truncation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Zusammmenfassung

Wir geben eine explizite Abschätzung der Konvergenzgeschwindigkeit einer endlichdimensionalen Fourier-Hermite-Entwicklung gegen die Lösung der Vlasov-Poisson-Gleichung für den räumlich 2-dimensionalen periodischen Fall an.

This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    T. P. Armstrong, R. C. Harding, G. Knorr and D. Montgomery,Solution of Vlasov's equation by transform methods in Methods in Computational Physics, ed. by B. Alder, S. Fernbach, M. Rotenberg, Academic Press New York, San Francisco, London 1970.Google Scholar
  2. [2]
    J. T. Beale and A. Majda,Vortex Methods I: Convergence in three dimensions, Vortex Methods II: Higher order accuracy in two and three dimensions. Math. of Comput.39, 1–27, 29–52 (1982).Google Scholar
  3. [3]
    J. Cooper,Galerkin approximations for the one-dimensional Vlasov-Poisson equation. Math. Meth. Appl. Sci.5, 516–529 (1983).Google Scholar
  4. [4a]
    O. Hald,The convergence of vortes methods II, SIAM J. Numer. Anal.16, 726–755 (1979).Google Scholar
  5. [4b]
    O. Hald,Convergence of Fourier methods for Navier-Stokes equations, J. Comp. Phys.40, 305–317 (1981).Google Scholar
  6. [5]
    E. Horst,On the classical solutions of the initial value problem for the unmodified non-linear Vlasov equation. Math. Meth. Appl. Sci.3, 229–248 (1981).Google Scholar
  7. [6]
    T. Kato,On classical solutions of the two-dimensional non-stationary Euler equation. Archiv. Rat. Mech. Anal.25, 188–200 (1967).Google Scholar
  8. [7]
    H. Neunzert and J. Wick,Die Theorie der asymptotischen Verteilung und die numerische Lösung von Integrodifferentialgleichungen, Num. Math.21, 234–243 (1973).Google Scholar
  9. [8]
    H. Neunzert,Neuere qualitative und numerische Methoden in der Plasmaphysik, Vorlesungsmanuskript Paderborn 1975.An introduction to the nonlinear Boltzmann-Vlasov equation in kinetic theories and the Boltzmann equation, ed. C. Cercignani, Lect. Notes in Maths 1048, Springer, Berlin 1984.Google Scholar
  10. [9]
    S. Ukai and T. Okabe,On classical solutions in the large in time of two-dimensional Vlasov's equation, Osaka J. Math.15, 245–261 (1978).Google Scholar
  11. [10]
    G. H. Cottet and P. A. Raviart,Particle methods for the one-dimensional Vlasov-Poisson equation, SIAM Num. Anal.21, 52–76 (1984).Google Scholar

Copyright information

© Birkhäuser Verlag Basel 1984

Authors and Affiliations

  • M. Pulvirenti
    • 1
  • J. Wick
    • 2
  1. 1.Dipt di Matematica dell'Università di Roma IRomaItaly
  2. 2.Fachbereich MathematikUniversität KaiserslauternKaiserslauternWest-Germany

Personalised recommendations