Chebyshev spectral approximation of Navier-Stokes equations in a two dimensional domain

Y. Maday; B. Métivet

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1987)

  • Volume: 21, Issue: 1, page 93-123
  • ISSN: 0764-583X

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Maday, Y., and Métivet, B.. "Chebyshev spectral approximation of Navier-Stokes equations in a two dimensional domain." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 21.1 (1987): 93-123. <http://eudml.org/doc/193499>.

@article{Maday1987,
author = {Maday, Y., Métivet, B.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Chebyshev approximation; Navier-Stokes equations; stream function form; convergence; pseudo-spectral numerical method; Optimal rate of convergence; polynomial approximation},
language = {eng},
number = {1},
pages = {93-123},
publisher = {Dunod},
title = {Chebyshev spectral approximation of Navier-Stokes equations in a two dimensional domain},
url = {http://eudml.org/doc/193499},
volume = {21},
year = {1987},
}

TY - JOUR
AU - Maday, Y.
AU - Métivet, B.
TI - Chebyshev spectral approximation of Navier-Stokes equations in a two dimensional domain
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1987
PB - Dunod
VL - 21
IS - 1
SP - 93
EP - 123
LA - eng
KW - Chebyshev approximation; Navier-Stokes equations; stream function form; convergence; pseudo-spectral numerical method; Optimal rate of convergence; polynomial approximation
UR - http://eudml.org/doc/193499
ER -

References

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  1. R. A., ADAMS, [1] Sobolev spaces; Academic Press (New York, San Francisco, London) 1975. Zbl0314.46030MR450957
  2. C. BASDEVANT, [1] Le modèle de simulation numérique de turbulence bidimensionnelle du L.M.D.; Note interne du L.M.D. n° 114 (juin 1982). 
  3. J. BERGH, J. LOFSTROM, [1] Interpolation spaces - an introduction; Springer-Verlag (Berlin, Heidelberg, New York) 1976. Zbl0344.46071MR482275
  4. C. BERNARDI, C CANUTO, Y. MADAY&gt;, [1] Generalized inf-sup. condition for Chebyshevapproximation of the Navier-Stokes equations; ICASE report 1986-63. 
  5. C. BERNARDI, Y. MADAY, B. MÉTIVET, [1] Spectral approximation of periodic/non periodic Navier-Stokes equations; to appear, in Numer. Math. Zbl0583.65085
  6. [2] Calcul de la pression dans la résolution spectrale du problème de Stokes. A paraître dans la « Recherche aérospatiale », 1986. 
  7. C. BERNARDI, G. RAUGEL, [1] Méthodes d'éléments finis mixtes pour les équations de Stokes et de Navier-Stokes dans un polygone convexe; Calcolo 18-3 (1981). Zbl0475.76035MR647827
  8. C. CANUTO, Y. MADAY, A. QUARTERONI, [1] Combined finite element and spectral approximation of the Navier-Stokes equations Numer. Math. 44, 201-217 (1984). Zbl0614.76021MR753953
  9. C. CANUTO, A. QUARTERONI, [1] Approximation Results for Orthogonal Polynomials in Sobolev Spaces, Math, of Comp. 38, (1981), 67-86. Zbl0567.41008MR637287
  10. J. DESCLOUX, J. RAPPAZ, [1] On numerical approximation of solution branches of nonlinear equations; R.A.I.R.O. Numer. Anal. 16-4, 319-350 (1982). Zbl0505.65016MR684829
  11. M. DEVILLE, L. KLEISER, F. MONTIGNY, [1] Pressure and time treatment of a Stokes problem, Int. Journal for Num. Methods in Fluids, 1984. Zbl0554.76033
  12. V. GIRAULT, P. A. RAVIART, [1] Finite Element Approximation of the Navier-Siokes equations, Theorie and Aigorithms ; Springer-Verlag (1986). Zbl0413.65081MR548867
  13. D. GOTTLIEB, S. A. ORSZAG, [1] Numericol analysis of spectral methods : Theory and applications; CBMSNS F Regional Conference Series in Applied Mathematics, SIAM, Philadelphie 1977. Zbl0412.65058MR520152
  14. P. GRISVARD, [1] Espaces intermédiaires entre espaces de Sobolev avec Poids; Ann.Scuola Norm. Sup. Pisa, 17, 1963. Zbl0117.08602MR160104
  15. L. KLEISER, U. SCHUMANN, [1] Treatment of Incompressibility and Boundary Conditions in 3-D Numerical Spectral Simulations of Plane Channel Flows, proceedings of the Third GAMM Conference on Numerical Methods in Huid Mechanics, Viewig-Verlag, Braunschweig (1980), 165-173. Zbl0463.76020
  16. P. LE QUERE, T. ALZIARY de ROQUEFORT, [1] Sur une méthode spectrale semi implicite pour la résolution des équations de Navier-Stokes d'un écoulement bidimensionnelvisqueux incompressible, C.R. Acad. Se. Paris, 294 (3 mai 1982), Série II, p. 941-944. Zbl0489.76037MR668777
  17. J. L. LIONS, [1] Quelques méthodes de résolution de problèmes aux limites non linéaires, Dunod, 1969. Zbl0189.40603MR259693
  18. Y. MADAY, [1] Analysis of spectral operators in one dimensional domain; ICASE report 1985, 17. 
  19. [2] Some spectral methods concerning a 4th order l-D problem ; to appear. 
  20. [3] Pseudo-spectral operators in multi-dimensional domains-application to Navier-Stokes problem; to appear. 
  21. Y. MADAY, B. MÉTIVET, [1] stimations d'erreur pour l'approximation des équations de Stokes par une méthode spectrale; la « Recherche aérospatiale », 4, (1983), p. 237 à 244. Zbl0523.76018MR729645
  22. Y. MADAY, A. QUARTERONI, [1] Spectral and pseudo-spectral approximations of Navier-Stokes équations; S.I.A.M. J. Numer. Anal 19(1982). Zbl0503.76035MR664883
  23. [2] Legendre and Chebyshev spectral approximation of Burger's équations; Numer.Math., 37 (1981). Zbl0452.41007MR627106
  24. [3] Approximation of Burger's equations by pseudo-spectral methods; R.A.I.R.O.An. Num. 16-4(1982). 
  25. M. R. MALIK, T. A. ZANG, M. Y. HUSSAINI, [1] A spectral collocation method for the Navier-Stokes equations, « ICASE Report » n° 84-19. Zbl0573.76036
  26. B. MÉTIVET, [1] Résolution des équations de Navier-Stokes par méthodes spectrales. Thèse, Université P. & M. Curie (1987). 
  27. B. MÉTIVET, Y. MORCHOISNE, [1] Multy domain spectral technique for viscous flow calculations. « ONERA » T. P, n° 1981-134. Zbl0515.76031
  28. Y. MORCHOISNE, [1] Résolution des équations de Navier-Stokes par méthode pseudo-spectrale en espace-temps; la « Recherche Aérospatiale » 5, (1979), pp. 293-306. Zbl0418.76026MR550092
  29. R. D. MOSER, P. MOIN A. LÉONARD, [1] A spectral numerical method for the Navier-Stokes equations with application to Taylor Couette flow; JCP - 52(1983), pp. 524-544. Zbl0529.76034MR727383
  30. S. A. ORSZAG, [1] Spectral methods for problems in complex geometries, J.C.P. 37 (1980), pp. 70-92. Zbl0476.65078MR584322
  31. S. A. ORSZAG, M. ISRAELI, M. DEVILLE, [1] Boundary Conditions for Incompressible Flows; to appear. Zbl0648.76023
  32. S. A. ORSZAG, A. T. PATERA, [1] Secondary instability of wall-bounded shear flows, J. Fluid Mech., 128 (1983). Zbl0556.76039
  33. R. VOIGT, D. GOTTLIEB, M. Y. HUSSAINI, [1] Proc. of Symposium on Spectral methods for Partial Differential Equations, SIAM Philadelphia (1984). MR758260

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