On conservative and entropic discrete axisymmetric Fokker-Planck operators
Frénod, Emmanuel ; Lucquin-Desreux, Brigitte
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 32 (1998), p. 307-339 / Harvested from Numdam
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Publié le : 1998-01-01
@article{M2AN_1998__32_3_307_0,
     author = {Fr\'enod, Emmanuel and Lucquin-Desreux, Brigitte},
     title = {On conservative and entropic discrete axisymmetric Fokker-Planck operators},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {32},
     year = {1998},
     pages = {307-339},
     mrnumber = {1627143},
     zbl = {0911.65136},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1998__32_3_307_0}
}

Frénod, Emmanuel; Lucquin-Desreux, Brigitte. On conservative and entropic discrete axisymmetric Fokker-Planck operators. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 32 (1998) pp. 307-339. http://gdmltest.u-ga.fr/item/M2AN_1998__32_3_307_0/

[1] M. Abrahamowitz & I. A. Stegun Handbook of mathematematical functions. Dover Publications, INC, New York.

[2] V. V. Aristov & F. G. Cheremisin, 1980, The conservative splitting method for solving Boltzmann's equation. U.S.R.R. Comput. Maths. Math. Phys., Vol. 20, No. 1, p. 208-225. | MR 564789 | Zbl 0458.76061

[3] A. A. Arsenev & O. E. Buryak, 1991, On the connection between a solution of the Boltzmann equation and a solution of the Landau-Fokker-Planck equation. Math. U.S.S.R. Sbornik, Vol. 69, No. 2, p. 465-478. | MR 1055522 | Zbl 0724.35090

[4] A. A. Arsenev & N. V. Peskov, 1978, On the existence of a generalized solution of Landau's equation. U.S.S.R. Comput. Maths. Math. Phys., Vol. 17, p. 241-246. | MR 470442 | Zbl 0383.35064

[5] Yu. A. Berezin, M. S. Pekker & V. N. Kudick, 1987, Conservative Finite-Difference Schemes for the Fokker-Planck Equation Not Violating the Low of an Increasing Entropy. Jour. of comp. phys., Vol. 69, p. 163-174. | MR 892257 | Zbl 0644.76091

[6] R. L. Berger, J. R. Albritton, C. J. Randall, E. A. Williams, W. L.Kruer, A. B.Langdon & C. J.Hanna, 1990, Stopping and thermahzation of interpenetrating plasma streams. Phys. Fluids B, Vol. 3, No. 1.

[7] A. V. Bobylev, 1981, Expansion of the Boltzmann collision integral in a Laudau series. Sov. Phys. Dolk., Vol. 20, No. 11, p. 740-742.

[8] A. V. Bobylev, I. F. Potapenko & V. A. Chuyanov, Kinetic equations of the Landau type as a model of the Boltzmann equation and completely conservative difference schemes. U.S.R.R. Comput. Maths. Math. Phys., Vol. 20, No. 4, p. 190-201. | MR 585294 | Zbl 0493.76078

[9] D. Deck & G. Samba, 1994, Le code Procions. Note CEA No. N 2780, CEA/CEL-V, F-94195 Villeneuve St. Georges Cedex.

[10] L. Desvillettes, 1992, On asymptotics of the Boltzmann equation when the collisions become grazing. Trans. Th. and Stat. Phys., Vol. 21, No. 3, p. 259-276. | MR 1165528 | Zbl 0769.76059

[11] P. Degond & B. Lucquin-Desreux, 1992, The Fokker-Plank assymptotics of the Boltzmann operator in the Coulomb case. Math. Mod. and Meth. in Appl. Sc., Vol. 2, No. 2, p. 167-182. | MR 1167768 | Zbl 0755.35091

[12] P. Degond & B. Lucquin-Desreux, 1994, An entropy scheme for the Fokker-Planck collision operator of plasma kinetic theory. Numer. Math., Vol. 68, p. 239-262. | MR 1283340 | Zbl 0806.65133

[13] I. S. Gradshteyn & I. M. Ryzhik, Table of integrals, series and products. Academic press. | MR 1773820 | Zbl 0918.65002

[14] N. A. Krall & A. W. Trivelpiece, 1973, Principles of plasma physics. Mc Graw Hill book company.

[15] S. Jorna & L. Wood, 1987, Fokker-Planck calculations on relaxation of anisotropic velocity distributions in plasmas. Phys. rev. A, Vol. 36, No. 1.

[16] O. Larroche, 1993, Kinetic simulation of a plasma collision experiment. Phys. Fluids B, Vol. 5, No. 8.

[17] M. Lemou, C. Buet, S. Cordier & P. Degond, A numerical, conservative and entropic scheme for the Fokker-Planck equation. In preparation.

[18] B. Lucquin-Desreux, 1992, Discrétisation de l'opérateur de Fokker-Planck dans le cas homogène. C. R. Acad. Sci., Paris, t. 314, p. 407-411. | MR 1153725 | Zbl 0749.35034

[19] W. M. Mac Donald, M. N. Rosenbluth & W. Chuck, 1957, Relaxation of a system of particles with Coulomb interactions. Phys. Rev., Vol. 107, No. 2. | MR 87304 | Zbl 0085.44701

[20] M. S. Pekker & V. N. Kudick, 1984, Conservative Difference Schemes for the Fokker-Planck Equation. U.S.R.R. Comput. Maths. Math. Phys., Vol. 24, No. 3, p. 206-210. | MR 750108

[21] I. F. Potapenko & V. A. Chuyanov, 1979, A completely conservative difference scheme for the two-dimensional Landau equation. U.S.R.R. Comput. Math. Math. Phys., Vol. 20, No. 2, p. 249-253. | MR 572407

[22] J. C. Witney, 1970, Finite Difference Methods for the Fokker-Planck Equation. J. Comp. Phys., Vol. 6, p. 483-509. | MR 273833 | Zbl 0203.48501