A spectral-Tau approximation for the Stokes and Navier-Stokes equations

Jie Shen

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1988)

  • Volume: 22, Issue: 4, page 677-693
  • ISSN: 0764-583X

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Shen, Jie. "A spectral-Tau approximation for the Stokes and Navier-Stokes equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 22.4 (1988): 677-693. <http://eudml.org/doc/193546>.

@article{Shen1988,
author = {Shen, Jie},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {spectral-Tau formulation; Stokes problem; pressure approximation; spurious modes; spectral convergence},
language = {eng},
number = {4},
pages = {677-693},
publisher = {Dunod},
title = {A spectral-Tau approximation for the Stokes and Navier-Stokes equations},
url = {http://eudml.org/doc/193546},
volume = {22},
year = {1988},
}

TY - JOUR
AU - Shen, Jie
TI - A spectral-Tau approximation for the Stokes and Navier-Stokes equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1988
PB - Dunod
VL - 22
IS - 4
SP - 677
EP - 693
LA - eng
KW - spectral-Tau formulation; Stokes problem; pressure approximation; spurious modes; spectral convergence
UR - http://eudml.org/doc/193546
ER -

References

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  2. [2] F. BREZZI, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers; Raior. Anal. Numer. 8-R2 129-151 (1974). Zbl0338.90047MR365287
  3. [3] C. BERNARDI, C. CANUTO & Y. MADAY, Generalized inf-sup condition for Chebychev approximation of the Navier-Stokes equations; IAN Report, N. 533, Pavia, Italy (1986). 
  4. [4] C. BERNARDI, Y. MADAY & B. MÉTIVET, Spectral approximation of the periodic non-periodic Navier-Stokes equations; to appear in Numer. Math. Zbl0583.65085MR914344
  5. [5] C. BERNARDI, Y. MADAY & B. MÉTIVET, Calcul de la pression dans la résolution spectrale des problèmes de Sotkes; La Recherche Aérospatiale, No. 1, 1-21 (1987). Zbl0642.76037MR904608
  6. [6] C. CANUTO & A. QUARTERONI, Spectral & pseudo-spectral methods for parabolic problems with non-periodic boudary conditions; Calcolo, vol. XVIII, fasi. III (1981). Zbl0485.65078MR647825
  7. [7] C. CANUTO & A. QUARTERONI, Approximation results for orthogonal polynomials in Sobolev spaces; Math. Comp. vol. 38, No. 157, 67-86 (1982). Zbl0567.41008MR637287
  8. [8] U. EHRENSTEIN, Méthodes spectrales de résolution des équations de Stokes et de Navier-Stokes. Application à des écoulements de convection double diffusive; Thèse, univ. de Nice (1986). 
  9. [9] V. GIRAULT & P. A. RAVIART, Finite element approximation of the Navier-Stokes equations; Springer-Verlag (1986). Zbl0413.65081MR548867
  10. [10] P. HALDENWANG, G. LABROSSE, S. ABBOUDI & M. DEVILLE, Chebychev 3-D and 2-D pseudo-spectral solver for the Helmholtz equations; J. Comp. Phy. vol. 55, 115-128 (1984). Zbl0544.65071MR757426
  11. [11] D. B. HAIDVOGEL & T. ZANG, The accurate solution of Poisson equation in Chebychev polynomials; J. Comp. Phy. vol. 30, 167-180 (1979). Zbl0397.65077MR528198
  12. [12] L. KLEISER & SCHUMANN, Treatment of incomppressibility and boundary conditions in 3-D numerical spectral simulation of plane channel flow; Proc. of the 3th GAMM conference on numer. methods in fluid mechanics, Viewig-Verlag Braunschweig, 165-173 (1980). Zbl0463.76020
  13. [13] G. SACCHI LANDERIANI, Spectral Tau approximation of the two dimensional Stokes problem; IAN Report, No. 528, Pavia, Italy (1986). Zbl0629.76037
  14. [14] R. TEMAM, Navier-Stokes equations. Theory and numerical analysis; North-Holland (1979). Zbl0426.35003
  15. [15] L. B. ZHANG, Thèse, univ. de Paris-sud (1987). 

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