Acta Mathematicae Applicatae Sinica

, Volume 7, Issue 3, pp 257–271 | Cite as

Spectral-finite element method for solving two-dimensional vorticity equations

  • Guo Benyu 
  • Cao Weiming 


In this paper, we construct a spectral-finite element scheme for solving semi-periodical two-dimensional vorticity equations. The error between the genuine solution and approximate solution is estimated strictly. The numerical results show the advantages of such a method. The technique used in this paper can be easily generalized to three-dimensional problems.


Approximate Solution Math Application Element Scheme Vorticity Equation Genuine Solution 
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  1. [1]
    Roache, P.J., Computational Fluid Dynamics, 2nd edition, Hermosa Publishers, 1976.Google Scholar
  2. [2]
    Raviart, P.A., Approximation numèrique des phenomenes de diffusion convection, Méthods d'éléments finis en méchanque des fluids, Cours a l'École d'été d'analyse numérique, 1979.Google Scholar
  3. [3]
    Guo Ben-yu, A Class of Difference Schemes for Two-dimensional Viscous Vorticity Equations,Acta Mathematica Sinica,17(1974), 242–258.Google Scholar
  4. [4]
    Guo Ben-yu, Error Estimation of Spectral Method for Solving Two-dimensional Vorticity Equations,J. Comp. Math.,1(1983), 353–362.Google Scholar
  5. [5]
    Guo Ben-yu, Spectral-difference Method for Solving Two-dimensional Vorticity Equations,J. Comp. Math.,6(1988), 238–257.Google Scholar
  6. [6]
    Canuto, C., Maday, Y., Quarteroni, A., Analysis of the Combined Finite Element and Fourier Interpolation,Numer. Math.,39(1982), 205–220.CrossRefGoogle Scholar
  7. [7]
    Canuto, C., Maday, Y., Quarteroni, A., Combined Finite Element and Spectral Approximation of the Navier-Stokes Equations, Numer. Math.,44(1984), 201–217.CrossRefGoogle Scholar
  8. [8]
    Mercier, B., Raugel, G., Résolution d'un probléme aux limites dans un ouvert axisymétrique par éléments finis enr, z et séries de Fourier enθ, RAIRO Numer. Anal.,16(1982), 405–461.Google Scholar
  9. [9]
    Ciarlet, P.G., The Finite-Element Method for Elliptic Problems, North-Holland, 1978.Google Scholar
  10. [10]
    Grisvard, P., Equations Differentielles Abstraites,Ann. Sci. Ecole Norm. Sup.,4 (1969), 311–395.Google Scholar

Copyright information

© Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A. 1991

Authors and Affiliations

  • Guo Benyu 
    • 1
  • Cao Weiming 
    • 1
  1. 1.Shanghai University of Science and TechnologyShanghai

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