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.
@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},
     pages = {227--285},
     publisher = {Gauthier-Villars},
     volume = {5},
     number = {3},
     year = {1988},
     mrnumber = {954473},
     zbl = {0688.76017},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1988__5_3_227_0/}
}
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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 | Zbl

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

[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 | Zbl

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

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

[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 | Zbl

[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

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

[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 | Zbl

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

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

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