A new approach for the analysis of Vortex Methods in two and three dimensions
Annales de l'I.H.P. Analyse non linéaire, Volume 5 (1988) no. 3, p. 227-285
@article{AIHPC_1988__5_3_227_0,
author = {Cottet, Georges-Henri},
title = {A new approach for the analysis of Vortex Methods in two and three dimensions},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Gauthier-Villars},
volume = {5},
number = {3},
year = {1988},
pages = {227-285},
zbl = {0688.76017},
mrnumber = {954473},
language = {en},
url = {http://www.numdam.org/item/AIHPC_1988__5_3_227_0}
}

Cottet, Georges-Henri. A new approach for the analysis of Vortex Methods in two and three dimensions. Annales de l'I.H.P. Analyse non linéaire, Volume 5 (1988) no. 3, pp. 227-285. http://www.numdam.org/item/AIHPC_1988__5_3_227_0/

[1] C. Anderson, A Vortex Method for Flows with Slight Density Variations, J. Comp. Phys., Vol. 61, 1985, pp. 417-432. | MR 816663 | Zbl 0576.76023

[2] J.T. Beale, A Convergent 3-D Vortex Method with Grid-Free Stretching, Math. Comp., Vol. 46, 1986, pp. 401-424. | MR 829616 | Zbl 0602.76024

[3] J.T. Beale and A. Majda, Rates of Convergence for Viscous Splitting of the Navier-Stokes Equations, Math. Comp., Vol. 31, 1981, pp. 243-259. | MR 628693 | Zbl 0518.76027

[4] J.T. Beale and A. Majda, Vortex Methods I: Convergence in Three Dimensions, Math. Comp., Vol. 39, 1982, pp. 1-27. | MR 658212 | Zbl 0488.76024

[5] L. Bers, F. John and M. Schechter, Partial Differential Equations, American Mathematical Society, Providence, 1964. | MR 163043 | Zbl 0514.35001

[6] G.H. Cottet, Convergence of a Vortex in Cell Method for the Two Dimensional Euler Equations, Math. Comp., vol. 40, 1987, pp. 407-425. | MR 906179 | Zbl 0652.65068

[7] G.H. Cottet and S. Mas-Gallic, A Particle Method to Solve Transport-Diffusion Equations II: the Navier-Stokes Equations, preprint.

[8] J. Goodman, Convergence of the Random Vortex Method, preprint. | MR 872384

[9] C. Greengard, Convergence of the Vortex Filament Method, Math. Comp., Vol. 47, 1986, pp. 387-398. | MR 856692 | Zbl 0617.65128

[10] P. Grisvard, Behaviour of the Solutions of an Elliptic Boundary Value Problem in a Polygonal or Polyhedral Domain, in Numerical Solutions of Partial Differential Equations III, Synspade, Academic Press, New York, 1976. | MR 466912 | Zbl 0361.35022

[11] O. Hald, The Convergence of Vortex Methods II, S.I.A.M. J. Num. Anal., Vol. 16, 1979, pp. 726-755. | MR 543965 | Zbl 0427.76024

[12] T. Kato, Nonstationary Flows of Viscous and Ideal Fluids in R3, J. Func. Anal., Vol. 9, 1962, pp. 296-305. | MR 481652 | Zbl 0229.76018

[13] J.-L. Lions and E. Magenes, Problemi ai limiti non omogenei, Ann. Sc. Norm. Sup. di Pisa, (III), Vol. 15, 1961, pp. 39-101 and (V), Vol. 16, 1962, pp. 1-14. | Numdam | MR 146527 | Zbl 0115.31401

[14] S. Mas-Gallic and P.A. Raviart, Particle Approximation of Convection-Diffusion Problems, Math. Comp. (submitted).

[15] R. Ranacher and R. Scott, Some Optimal Error Estimates for Piecewise Linear Finite Element Approximations, Math. Comp., Vol. 38, 1982, pp. 437-446. | MR 645661 | Zbl 0483.65007

[16] P.A. Raviart, An Analysis of Particle Methods, in Numerical Methods in Fluid Dynamics, F. BREZZI Ed., Lecture Notes in Mathematics, vol. 1127, Springer Verlag, Berlin, 1985. | MR 802214 | Zbl 0598.76003

[17] J. Soler, On the Vortex Filament Method, preprint. | MR 1036649