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Analysis of a high order finite volume scheme for the 1D Vlasov-Poisson system
1. | Université Lyon, Université Lyon1, CNRS, UMR 5208 - Institut Camille Jordan, 43, Boulevard du 11 Novembre 1918, F-69622 Villeurbanne cedex, France |
2. | Université Bordeaux I, UMR CELIA CEA, CNRS et Institut de Mathmatiques de Bordeaux, 351, Cours de la Libération, F-33405 Talence cedex, France, France |
References:
[1] |
T. D. Arber and R. G. L. Vann, A critical comparison of Eulerian-grid-based Vlasov solvers, J. Comput. Physics, 180 (2002), 339-357.
doi: 10.1006/jcph.2002.7098. |
[2] |
N. Besse, Convergence of a semi-Lagrangian scheme for the one-dimensional Vlasov-Poisson system, SIAM J. Numer. Anal., 42 (2004), 350-382.
doi: 10.1137/S0036142902410775. |
[3] |
J. P. Boris and D. L. Book, Solution of continuity equations by the method of flux-corrected transport, J. Comput. Phys., 20 (1976), 397-431.
doi: 10.1016/0021-9991(76)90091-7. |
[4] |
J. A. Carrillo and F. Vecil, Nonoscillatory interpolation methods applied to Vlasov-based models, SIAM J. Sci. Comput., 29 (2007), 1179-1206.
doi: 10.1137/050644549. |
[5] |
C. Z. Cheng and G. Knorr, The integration of the Vlasov equation in configuration space, J. Comput. Phys., 22 (1976), 330-351.
doi: 10.1016/0021-9991(76)90053-X. |
[6] |
J. Cooper and A. J. Klimas, Boundary value problems for the Vlasov-Maxwell equation in one dimension, J. Math. Anal. Appl., 75 (1980), 306-329.
doi: 10.1016/0022-247X(80)90082-7. |
[7] |
P. Degond and P.-A. Raviart, An asymptotic analysis of the Vlasov-Poisson system: The Child-Langmuir law, Asymptotic Anal., 4 (1991), 187-214. |
[8] |
R. J. DiPerna and P. L. Lions, Solutions globales d'équations du type Vlasov-Poisson, C. R. Acad. Sci. Paris Série I Math., 307 (1988), 306-329. |
[9] |
F. Filbet, Convergence d'un schéma de type volumes finis pour la resolution numérique du système de Vlasov-Poisson en dimension un, (French) [Convergence of a finite volume scheme for the numerical solution of the one-dimensional Vlasov-Poisson system], CRAS Paris, 330 (2000), 979-984. |
[10] |
F. Filbet, Convergence of a finite volume scheme for the Vlasov-Poisson system, SIAM J. Numer. Anal. 39 (2001), 1146-1169.
doi: 10.1137/S003614290037321X. |
[11] |
F. Filbet, E. Sonnendrücker and P. Bertrand, Conservative numerical schemes for the Vlasov equation, J. Comput. Phys. 172 (2001), 166-187.
doi: 10.1006/jcph.2001.6818. |
[12] |
F. Filbet and E. Sonnendrücker, Comparison of Eulerian Vlasov solvers, Computer Physics Communications, 150 (2003), 247-266.
doi: 10.1016/S0010-4655(02)00694-X. |
[13] |
F. Filbet, Y. Guo and C.-W. Shu, Analysis of the relativistic Vlasov-Maxwell model in an interval, Quarterly Applied Math., 63 (2005), 691-714. |
[14] |
C. Greengard and P.-A. Raviart, A boundary-value problem for the stationary Vlasov-Poisson equations: The plane diode, Comm. Pure. Appl. Math., 43 (1990), 473-507.
doi: 10.1002/cpa.3160430404. |
[15] |
Y. Guo, Global weak solutions of the Vlasov-Maxwell system with boundary conditions, Comm. Math. Phys., 154 (1993), 254-263.
doi: 10.1007/BF02096997. |
[16] |
Y. Guo, C.-W. Shu and T. Zhou, The dynamics of a plane diode, SIAM J. Math. Anal., 35 (2004), 1617-1635.
doi: 10.1137/S0036141003421133. |
[17] |
A. J. Klimas and W. M. Farrell, A splitting algorithm for Vlasov simulation with filamentation filtration, J. Comput. Phys., 110 (1994), 150-163.
doi: 10.1006/jcph.1994.1011. |
[18] |
F. Poupaud, Boundary value problems for the stationary Vlasov-Maxwell system, Forum Math., 4 (1992), 499-527.
doi: 10.1515/form.1992.4.499. |
[19] |
J. Schaeffer, Convergence of a difference scheme for the Vlasov-Poisson-Fokker-Planck system in one dimension, SIAM J. Numer. Anal., 35 (1998), 1149-1175.
doi: 10.1137/S0036142996302554. |
[20] |
M. Shoucri and G. Knorr, Numerical integration of the Vlasov equation, J. Comput. Phys., 14 (1974), 84-92.
doi: 10.1016/0021-9991(74)90006-0. |
[21] |
Y. Zheng and A. Majda, Existence of global weak solutions to one-component Vlasov-Poisson and Fokker-Planck-Poisson systems in one space dimension with measures as initial data, Comm. Pure Appl. Math., 47 (1994), 1365-1401.
doi: 10.1002/cpa.3160471004. |
[22] |
T. Nakamura and T. Yabe, Cubic interpolated propagation scheme for solving the hyper-dimensional Vlasov-Poisson equation in phase space, Comput. Phys. Communications, 120 (1999), 122-154.
doi: 10.1016/S0010-4655(99)00247-7. |
show all references
References:
[1] |
T. D. Arber and R. G. L. Vann, A critical comparison of Eulerian-grid-based Vlasov solvers, J. Comput. Physics, 180 (2002), 339-357.
doi: 10.1006/jcph.2002.7098. |
[2] |
N. Besse, Convergence of a semi-Lagrangian scheme for the one-dimensional Vlasov-Poisson system, SIAM J. Numer. Anal., 42 (2004), 350-382.
doi: 10.1137/S0036142902410775. |
[3] |
J. P. Boris and D. L. Book, Solution of continuity equations by the method of flux-corrected transport, J. Comput. Phys., 20 (1976), 397-431.
doi: 10.1016/0021-9991(76)90091-7. |
[4] |
J. A. Carrillo and F. Vecil, Nonoscillatory interpolation methods applied to Vlasov-based models, SIAM J. Sci. Comput., 29 (2007), 1179-1206.
doi: 10.1137/050644549. |
[5] |
C. Z. Cheng and G. Knorr, The integration of the Vlasov equation in configuration space, J. Comput. Phys., 22 (1976), 330-351.
doi: 10.1016/0021-9991(76)90053-X. |
[6] |
J. Cooper and A. J. Klimas, Boundary value problems for the Vlasov-Maxwell equation in one dimension, J. Math. Anal. Appl., 75 (1980), 306-329.
doi: 10.1016/0022-247X(80)90082-7. |
[7] |
P. Degond and P.-A. Raviart, An asymptotic analysis of the Vlasov-Poisson system: The Child-Langmuir law, Asymptotic Anal., 4 (1991), 187-214. |
[8] |
R. J. DiPerna and P. L. Lions, Solutions globales d'équations du type Vlasov-Poisson, C. R. Acad. Sci. Paris Série I Math., 307 (1988), 306-329. |
[9] |
F. Filbet, Convergence d'un schéma de type volumes finis pour la resolution numérique du système de Vlasov-Poisson en dimension un, (French) [Convergence of a finite volume scheme for the numerical solution of the one-dimensional Vlasov-Poisson system], CRAS Paris, 330 (2000), 979-984. |
[10] |
F. Filbet, Convergence of a finite volume scheme for the Vlasov-Poisson system, SIAM J. Numer. Anal. 39 (2001), 1146-1169.
doi: 10.1137/S003614290037321X. |
[11] |
F. Filbet, E. Sonnendrücker and P. Bertrand, Conservative numerical schemes for the Vlasov equation, J. Comput. Phys. 172 (2001), 166-187.
doi: 10.1006/jcph.2001.6818. |
[12] |
F. Filbet and E. Sonnendrücker, Comparison of Eulerian Vlasov solvers, Computer Physics Communications, 150 (2003), 247-266.
doi: 10.1016/S0010-4655(02)00694-X. |
[13] |
F. Filbet, Y. Guo and C.-W. Shu, Analysis of the relativistic Vlasov-Maxwell model in an interval, Quarterly Applied Math., 63 (2005), 691-714. |
[14] |
C. Greengard and P.-A. Raviart, A boundary-value problem for the stationary Vlasov-Poisson equations: The plane diode, Comm. Pure. Appl. Math., 43 (1990), 473-507.
doi: 10.1002/cpa.3160430404. |
[15] |
Y. Guo, Global weak solutions of the Vlasov-Maxwell system with boundary conditions, Comm. Math. Phys., 154 (1993), 254-263.
doi: 10.1007/BF02096997. |
[16] |
Y. Guo, C.-W. Shu and T. Zhou, The dynamics of a plane diode, SIAM J. Math. Anal., 35 (2004), 1617-1635.
doi: 10.1137/S0036141003421133. |
[17] |
A. J. Klimas and W. M. Farrell, A splitting algorithm for Vlasov simulation with filamentation filtration, J. Comput. Phys., 110 (1994), 150-163.
doi: 10.1006/jcph.1994.1011. |
[18] |
F. Poupaud, Boundary value problems for the stationary Vlasov-Maxwell system, Forum Math., 4 (1992), 499-527.
doi: 10.1515/form.1992.4.499. |
[19] |
J. Schaeffer, Convergence of a difference scheme for the Vlasov-Poisson-Fokker-Planck system in one dimension, SIAM J. Numer. Anal., 35 (1998), 1149-1175.
doi: 10.1137/S0036142996302554. |
[20] |
M. Shoucri and G. Knorr, Numerical integration of the Vlasov equation, J. Comput. Phys., 14 (1974), 84-92.
doi: 10.1016/0021-9991(74)90006-0. |
[21] |
Y. Zheng and A. Majda, Existence of global weak solutions to one-component Vlasov-Poisson and Fokker-Planck-Poisson systems in one space dimension with measures as initial data, Comm. Pure Appl. Math., 47 (1994), 1365-1401.
doi: 10.1002/cpa.3160471004. |
[22] |
T. Nakamura and T. Yabe, Cubic interpolated propagation scheme for solving the hyper-dimensional Vlasov-Poisson equation in phase space, Comput. Phys. Communications, 120 (1999), 122-154.
doi: 10.1016/S0010-4655(99)00247-7. |
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