Free access
Issue
ESAIM: M2AN
Volume 44, Number 3, May-June 2010
Page(s) 573 - 595
DOI http://dx.doi.org/10.1051/m2an/2010012
Published online 04 February 2010
  1. R.P. Agarwal, Difference equations and inequalities, Monographs and Textbooks in pure and applied mathematics. Marcel Dekker, New York, USA (1992).
  2. H. Andréasson and G. Rein, A numerical investigation of stability states and critical phenomena for the spherically symmetric Einstein-Vlasov system. Class. Quant. Grav. 23 (2006) 3659–3677. [CrossRef]
  3. F. Bastin and P. Laubin, Regular compactly supported wavelets in Sobolev spaces. Duke Math. J. 87 (1996) 481–508. [CrossRef]
  4. M.L. Bégué, A. Ghizzo, P. Bertrand, E. Sonnendrücker and O. Coulaud, Two dimensional semi-Lagrangian Vlasov simulations of laser-plasma interaction in the relativistic regime. J. Plasma Phys. 62 (1999) 367–388. [CrossRef]
  5. N. Besse, Convergence of a semi-Lagrangian scheme for the one-dimensional Vlasov-Poisson system. SIAM J. Numer. Anal. 42 (2004) 350–382. [CrossRef] [MathSciNet]
  6. N. Besse, Convergence of a high-order semi-Lagrangian scheme with propagation of gradients for the Vlasov-Poisson system. SIAM J. Numer. Anal. 46 (2008) 639–670. [CrossRef] [MathSciNet]
  7. N. Besse and P. Bertrand, Gyro-water-bag approch in nonlinear gyrokinetic turbulence. J. Comput. Phys. 228 (2009) 3973–3995. [CrossRef] [MathSciNet]
  8. N. Besse and M. Mehrenberger, Convergence of classes of high-order semi-Lagrangian schemes for the Vlasov-Poisson system. Math. Comp. 77 (2008) 93–123. [CrossRef] [MathSciNet]
  9. N. Besse and E. Sonnendrücker, Semi-Lagrangian schemes for the Vlasov equation on an unstructured mesh of phase space. J. Comput. Phys. 191 (2003) 341–376. [CrossRef] [MathSciNet]
  10. N. Besse, G. Latu, A. Ghizzo, E. Sonnendrücker and P. Bertrand, A Wavelet-MRA-based adaptive semi-Lagrangian method for the relativistic Vlasov-Maxwell system. J. Comput. Phys. 227 (2008) 7889–7916. [CrossRef] [MathSciNet]
  11. C.K. Birdsall and A.B. Langdon, Plasmas physics via computer simulation. McGraw-Hill, USA (1985).
  12. C.Z. Cheng and G. Knorr, The integration of the Vlasov equation in configuration space. J. Comput Phys. 22 (1976) 330–351. [CrossRef]
  13. M.W. Choptuik, Universality and scaling in gravitational collapse of a scalar field. Phys. Rev. Lett. 70 (1993) 9–12. [CrossRef] [PubMed]
  14. M.W. Choptuik and I. Obarrieta, Critical phenomena at the threshold of black hole formation for collisionless matter in spherical symmetry. Phys. Rev. D 65 (2001) 024007. [CrossRef]
  15. M.W. Choptuik, T. Chmaj and P. Bizoń, Critical behaviour in gravitational collapse of a Yang-Mills field. Phys. Rev. Lett. 77 (1996) 424–427. [CrossRef] [PubMed]
  16. Y. Choquet-Bruhat, Problème de Cauchy pour le système intégro-différentiel d'Einstein–Liouville. Ann. Inst. Fourier 21 (1971) 181–201.
  17. A. Cohen, Numerical analysis of wavelet methods, Studies in mathematics and its applications 32. Elsevier, North-Holland (2003).
  18. J.M. Dawson, Particle simulation of plasmas. Rev. Modern Phys. 55 (1983) 403–447. [NASA ADS] [CrossRef]
  19. K. Ganguly and H. Victory, On the convergence for particle methods for multidimensional Vlasov-Poisson systems. SIAM J. Numer. Anal. 26 (1989) 249-288. [CrossRef] [MathSciNet]
  20. R.T. Glassey and J. Schaeffer, Convergence of a particle method for the relativistic Vlasov-Maxwell system. SIAM J. Numer. Anal. 28 (1991) 1–25. [CrossRef] [MathSciNet]
  21. G. Rein and A.D. Rendall, Global existence of solutions of the spherically symmetric Vlasov-Einstein with small initial data. Commun. Math. Phys. 150 (1992) 561–583. [Erratum. Comm. Math. Phys. 176 (1996) 475–478.] [CrossRef]
  22. G. Rein and T. Rodewis, Convergence of a Particle-In-Cell scheme for the spherically symmetric Vlasov-Einstein system. Ind. Un. Math. J. 52 (2003) 821–861.
  23. G. Rein, A.D. Rendall and J. Schaeffer, A regularity theorem for solutions of the spherical symmetric Vlasov-Einstein system. Commun. Math. Phys. 168 (1995) 467–478. [CrossRef]
  24. G. Rein, A.D. Rendall and J. Schaeffer, Critical collapse of collisionless matter-a numerical investigation. Phys. Rev. D 58 (1998) 044007. [CrossRef]
  25. T. Rodewis, Numerical treatment of the symmetric Vlasov-Poisson and Vlasov-Einstein system by particle methods. Ph.D. Thesis, Mathematisches Institut der Ludwig-Maximilians-Universität München, Munich, Germany (1999).
  26. J. Schaeffer, Discrete approximation of the Poisson-Vlasov system. Quart. Appl. Math. 45 (1987) 59–73. [MathSciNet]
  27. S.L. Shapiro and S.A. Teukolsky, Relativistic stellar dynamics on computer I, Motivation and numerical methods. Astrophys. J. 298 (1985) 34–57. [CrossRef]
  28. S.L. Shapiro and S.A. Teukolsky, Relativistic stellar dynamics on computer II, Physical applications. Astrophys. J. 298 (1985) 58–79. [CrossRef]
  29. S.L. Shapiro and S.A. Teukolsky, Relativistic stellar dynamics on computer IV, Collapse of a stellar cluster to a black hole. Astrophys. J. 307 (1986) 575–592. [CrossRef]
  30. A. Staniforth and J. Cote, Semi-Lagrangian integration schemes for atmospheric models-a review. Mon. Weather Rev. 119 (1991) 2206–2223. [CrossRef]
  31. H.D. Victory and E.J. Allen, The convergence theory of particle-in-cell methods for multi-dimensional Vlasov-Poisson systems. SIAM J. Numer. Anal. 28 (1991) 1207–1241. [CrossRef] [MathSciNet]
  32. H.D. Victory, G. Tucker and K. Ganguly, The convergence analysis of fully discretized particle methods for solving Vlasov-Poisson systems. SIAM J. Numer. Anal. 28 (1991) 955–989. [CrossRef] [MathSciNet]

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