Free Access
Volume 34, Number 3, May/june 2000
Page(s) 637 - 662
Published online 15 April 2002
  1. C. Bernardi and Y. Maday, Spectral methods for the approximation of fourth order problems: Applications to the Stokes and Navier-Stokes equations. Comput. and Structures 30 (1988) 205-216. [CrossRef] [MathSciNet]
  2. C. Bernardi and Y. Maday, Some spectral approximations of one-dimensional fourth order problems, in: Progress in Approximation Theory, P. Nevai and A. Pinkus Eds., Academic Press, San Diego (1991), 43-116.
  3. C. Bernardi and Y. Maday, Spectral methods, in Handbook of Numerical Analysis, Vol. V, Part 2: Techniques of Scientific Computing, P.G. Ciarlet and J.L. Lions Eds., North-Holland, Amsterdam (1997) 209-485.
  4. C. Bernardi, G. Coppoletta and Y. Maday, Some spectral approximations of two-dimensional fourth order problems. Math. Comp. 59 (1992) 63-76. [CrossRef] [MathSciNet]
  5. B. Bialecki, A fast solver for the orthogonal spline collocation solution of the biharmonic Dirichlet problem on rectangles. submitted.
  6. P.E. Bjørstad and B.P. Tjøstheim, Efficient algorithms for solving a fourth-order equation with the spectral-Galerkin method. SIAM J. Sci. Comput. 18 (1997) 621-632. [CrossRef] [MathSciNet]
  7. J.P. Boyd, Chebyshev and Fourier Spectral Methods. Springer-Verlag, Berlin (1989).
  8. J. Douglas Jr. and T. Dupont, Collocation Methods for Parabolic Equations in a Single Space Variable. Lect. Notes Math. 358, Springer-Verlag, New York, 1974.
  9. G.H. Golub and C.F. van Loan, Matrix Computations, Third edn., The Johns Hopkins University Press, Baltimore, MD (1996).
  10. W. Heinrichs, A stabilized treatment of the biharmonic operator with spectral methods. SIAM J. Sci. Stat. Comput. 12 (1991) 1162-1172. [CrossRef]
  11. A. Karageorghis, The numerical solution of laminar flow in a re-entrant tube geometry by a Chebyshev spectral element collocation method. Comput. Methods Appl. Mech. Engng. 100 (1992) 339-358. [CrossRef]
  12. A. Karageorghis, A fully conforming spectral collocation scheme for second and fourth order problems. Comput. Methods Appl. Mech. Engng. 126 (1995) 305-314. [CrossRef]
  13. A. Karageorghis and T.N. Phillips, Conforming Chebyshev spectral collocation methods for the solution of laminar flow in a constricted channel. IMA Journal Numer. Anal. 11 (1991) 33-55. [CrossRef]
  14. A. Karageorghis and T. Tang, A spectral domain decomposition approach for steady Navier-Stokes problems in circular geometries. Computers and Fluids 25 (1996) 541-549. [CrossRef] [MathSciNet]
  15. Z.-M. Lou, B. Bialecki, and G. Fairweather, Orthogonal spline collocation methods for biharmonic problems. Numer. Math. 80 (1998) 267-303. [CrossRef] [MathSciNet]
  16. W.W. Schultz, N.Y. Lee and J.P. Boyd, Chebyshev pseudospectral method of viscous flows with corner singularities. J. Sci. Comput. 4 (1989) 1-19. [CrossRef]
  17. J. Shen, Efficient spectral-Galerkin method I. Direct solvers of second- and forth-order equations using Legendre polynomials. SIAM J. Sci. Comput. 15 (1994) 1489-1505. [CrossRef] [MathSciNet]

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