A new approach for the analysis of Vortex Methods in two and three dimensions

Georges-Henri Cottet

Annales de l'I.H.P. Analyse non linéaire (1988)

  • Volume: 5, Issue: 3, page 227-285
  • ISSN: 0294-1449

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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 5.3 (1988): 227-285. <http://eudml.org/doc/78153>.

@article{Cottet1988,
author = {Cottet, Georges-Henri},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {error estimates; linear first order hyperbolic equations; analysis of vortex methods; weak solution; convection deformation; Euler equations},
language = {eng},
number = {3},
pages = {227-285},
publisher = {Gauthier-Villars},
title = {A new approach for the analysis of Vortex Methods in two and three dimensions},
url = {http://eudml.org/doc/78153},
volume = {5},
year = {1988},
}

TY - JOUR
AU - Cottet, Georges-Henri
TI - A new approach for the analysis of Vortex Methods in two and three dimensions
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1988
PB - Gauthier-Villars
VL - 5
IS - 3
SP - 227
EP - 285
LA - eng
KW - error estimates; linear first order hyperbolic equations; analysis of vortex methods; weak solution; convection deformation; Euler equations
UR - http://eudml.org/doc/78153
ER -

References

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  1. [1] C. Anderson, A Vortex Method for Flows with Slight Density Variations, J. Comp. Phys., Vol. 61, 1985, pp. 417-432. Zbl0576.76023MR816663
  2. [2] J.T. Beale, A Convergent 3-D Vortex Method with Grid-Free Stretching, Math. Comp., Vol. 46, 1986, pp. 401-424. Zbl0602.76024MR829616
  3. [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. Zbl0518.76027MR628693
  4. [4] J.T. Beale and A. Majda, Vortex Methods I: Convergence in Three Dimensions, Math. Comp., Vol. 39, 1982, pp. 1-27. Zbl0488.76024MR658212
  5. [5] L. Bers, F. John and M. Schechter, Partial Differential Equations, American Mathematical Society, Providence, 1964. Zbl0514.35001MR163043
  6. [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. Zbl0652.65068MR906179
  7. [7] G.H. Cottet and S. Mas-Gallic, A Particle Method to Solve Transport-Diffusion Equations II: the Navier-Stokes Equations, preprint. Zbl0678.35077
  8. [8] J. Goodman, Convergence of the Random Vortex Method, preprint. MR872384
  9. [9] C. Greengard, Convergence of the Vortex Filament Method, Math. Comp., Vol. 47, 1986, pp. 387-398. Zbl0617.65128MR856692
  10. [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. Zbl0361.35022MR466912
  11. [11] O. Hald, The Convergence of Vortex Methods II, S.I.A.M. J. Num. Anal., Vol. 16, 1979, pp. 726-755. Zbl0427.76024MR543965
  12. [12] T. Kato, Nonstationary Flows of Viscous and Ideal Fluids in R3, J. Func. Anal., Vol. 9, 1962, pp. 296-305. Zbl0229.76018MR481652
  13. [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. Zbl0115.31401MR146527
  14. [14] S. Mas-Gallic and P.A. Raviart, Particle Approximation of Convection-Diffusion Problems, Math. Comp. (submitted). Zbl0863.76095
  15. [15] R. Ranacher and R. Scott, Some Optimal Error Estimates for Piecewise Linear Finite Element Approximations, Math. Comp., Vol. 38, 1982, pp. 437-446. Zbl0483.65007MR645661
  16. [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. Zbl0598.76003MR802214
  17. [17] J. Soler, On the Vortex Filament Method, preprint. Zbl0683.76024MR1036649

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