Streamline diffusion methods for the Vlasov-Poisson equation
ESAIM: Modélisation mathématique et analyse numérique, Tome 24 (1990) no. 2, pp. 177-196. 
@article{M2AN_1990__24_2_177_0,
     author = {Asadzadeh, Mohammad},
     title = {Streamline diffusion methods for the {Vlasov-Poisson} equation},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {177--196},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {24},
     number = {2},
     year = {1990},
     mrnumber = {1052146},
     zbl = {0703.76106},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1990__24_2_177_0/}
}
TY  - JOUR
AU  - Asadzadeh, Mohammad
TI  - Streamline diffusion methods for the Vlasov-Poisson equation
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1990
SP  - 177
EP  - 196
VL  - 24
IS  - 2
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://www.numdam.org/item/M2AN_1990__24_2_177_0/
LA  - en
ID  - M2AN_1990__24_2_177_0
ER  - 
%0 Journal Article
%A Asadzadeh, Mohammad
%T Streamline diffusion methods for the Vlasov-Poisson equation
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1990
%P 177-196
%V 24
%N 2
%I AFCET - Gauthier-Villars
%C Paris
%U http://www.numdam.org/item/M2AN_1990__24_2_177_0/
%G en
%F M2AN_1990__24_2_177_0
Asadzadeh, Mohammad. Streamline diffusion methods for the Vlasov-Poisson equation. ESAIM: Modélisation mathématique et analyse numérique, Tome 24 (1990) no. 2, pp. 177-196. http://www.numdam.org/item/M2AN_1990__24_2_177_0/

[1] A. A. Arsenev, Global existence of a weak solution of Vlasov's System of equations, U.S.S.R. Comput. Math, and Math. Phys., 15 (1975), pp. 131-143. | MR | Zbl

[2] A. A. Arsenev, Local uniqueness and existence of a classical solution of Vlasov's system of equations, Soviet Math. Dokl., 15 (1974), pp. 1223-1225. | Zbl

[3] C. Bardos and P. Degond, Global existence for the Vlasov Poisson equation in 3 space variables with small initial data. École Polytechnique, Centre de Mathématiques Appliquées, Rapport interne N° 101.

[4] J. T. Beal andA. Majda, Vortex methods I and II, Math. Comp., 32 (1982), pp. 1-27 and pp. 29-52.

[5] P. G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, 1978. | MR | Zbl

[6] G. H. CottetandP. A. Raviart, Particle methods for the one-dimensional Vlasov-Poisson equation, SIAM J. Numer., Anal., 21 (1984), pp. 52-76. | MR | Zbl

[7] G. H. Cottet and P. A. Raviart, On particle-in-cell methods for the Vlasov-Poisson equations, TTSP, 15 (1986) pp. 1-31. | MR

[8] J. Denavit, Pitfalls in particle simulations and in numerical solutions of the Vlasov equation, in Proceedings of the Oberwalfach Conference on Mathematical Methods of Plasma physics, ed. by R, Kress and J. Wick, 1980, Band 20, pp. 247-269. | Zbl

[9] J. Dugundji, Topology. Allyn and Bacon, Boston, 1966. | MR | Zbl

[10] P. Hansbo, Finite Element Procedures for Conduction and Convection Problems, Licenciat thesis, Chalmers Univ. of Technology, Department of Structural Mechanics, 1986.

[11] R. W. Hockney andJ. W. Eastwood, Computer Simulations, using Particles, McGraw-Hill, New York, 1981. | Zbl

[12] T. J. Hughes andA. Brooks, A multidimensional upwind scheme with no crosswind diffusion, in AMD, vol. 34, Finite Element Methods for Convection Dominated Flows, T. J. Hughes (ed.), ASME, New York, 1979. | MR | Zbl

[13] S. V. Iordanskii, The Cauchy problem for the kinetic equation of plasma, Trudy Mat. Inst. Steklow, 60 (1961), 181-194, English transl. Amer. Math. Soc.Trans. ser. 2, 35 (1964), pp. 351-363. | MR | Zbl

[14] C. Johnson, Finite element methods for convection-diffusion problems, in Computing Methods in Applied Science and Engineering, R. Glowinski, J. L.Lions (eds.) North-Holland, INRIA, 1982. | MR | Zbl

[15] C. Johnson and U. Nàvert, An analysis of some finite element methods for advection-diffusion, in Analytical and Numerical Approaches to Asymptotic Problems in Analysis, O. Axelsson, L. Frank and A. Van der Sluis (eds.), North-Holland, Amsterdam, 1981. | MR | Zbl

[16] C. Johnson,U. Nâvert and J. Pitkâranta, Finite element methods for linear hyperbolic problems, Comput. Methods in Appl. Mech. and Engineering, 45 (1985), pp. 285-312. | MR | Zbl

[17] C. Johnson and J. Saranen, Streamline diffusion methods for the incompressible Euler and Navier-Stokes equations, Math. Comp., 47 (1986), pp. 1-18. | MR | Zbl

[18] C. Johnson and A. Szepessy, On the convergence of a finite element method for a nonlinear hyperbolic conservation law, Math. Comp. vol. 49, 1987, pp. 427-444. | MR | Zbl

[19] J. L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod, Paris 1969. | MR | Zbl

[20] H. Neunzert and J. Wick, The convergence of simulation methods in plasma physics, in Proceedings of the Oberwalfach conference on Mathematical Methods of Plasma Physics, R. Kress and J. Wich (Verlag Peter Lang 1980), Band 20, pp. 272-286. | MR | Zbl

[21] U. Nàvert, A finite element method for convection-diffusion problems, Thesis,Chalmers Univ. of Technology, Göteborg, 1982.

[22] S. Ukai andT. Okabe, On classical solution in the large in time of two-dimensional Vlasov's équation, Osaka J. of Math., 15 (1978), pp. 245-261. | MR | Zbl

[23] A. A. Vlasov, Many Particle Theory and its Application to Plasma, State Publishing House for Technical-Theoretical Literature, Moscow and Leningrad, 1950, Gordon and Breach, Science publishers, Library of Congress, 1961. | MR

[24] S. Wollman, The use of a heat operator in an existence theory problem of the Vlasov equation, TTSP, 14 (1985), pp. 567-593. | MR | Zbl