A Legendre spectral collocation method for the biharmonic Dirichlet problem
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 34 (2000) no. 3, p. 637-662
@article{M2AN_2000__34_3_637_0,
author = {Bialecki, Bernard and Karageorghis, Andreas},
title = {A Legendre spectral collocation method for the biharmonic Dirichlet problem},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {Dunod},
volume = {34},
number = {3},
year = {2000},
pages = {637-662},
zbl = {0984.65121},
mrnumber = {1763529},
language = {en},
url = {http://www.numdam.org/item/M2AN_2000__34_3_637_0}
}

Bialecki, Bernard; Karageorghis, Andreas. A Legendre spectral collocation method for the biharmonic Dirichlet problem. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 34 (2000) no. 3, pp. 637-662. http://www.numdam.org/item/M2AN_2000__34_3_637_0/

[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. | MR 964358 | Zbl 0668.76038

[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. | MR 1114769

[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. | MR 1470226

[4] C. Bernardi, G. Coppoletta and Y. Maday, Some spectral approximations of two-dimensional fourth order problems. Math. Comp. 59 (1992) 63-76. | MR 1134714 | Zbl 0754.65088

[5] B. Bialecki, A fast solver for the orthogonal spline collocation solution of the biharmonic Dirichlet problem on rectangles. submitted | Zbl 1032.65134

[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. | MR 1433799 | Zbl 0939.65129

[7] J. P. Boyd, Chebyshev and Fourier Spectral Methods. Springer-Verlag, Berlin (1989). | Zbl 0681.65079

[8] J. Jr. Douglas and T. Dupont, Collocation Methods for Parabolic Equations in a Single Space Variable. Lect. Notes Math. 358, Springer-Verlag, New York, 1974. | MR 483559 | Zbl 0279.65097

[9] G. H. Golub and C. F. Van Loan, Matrix Computations, Third edn., The Johns Hopkins University Press, Baltimore, MD (1996). | MR 1417720 | Zbl 0865.65009

[10] W. Heinrichs, A stabilized treatment of the biharmonic operator with spectral methods. SIAM J. Sci. Stat. Comput. 12 (1991) 1162-1172. | MR 1114979 | Zbl 0729.65088

[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. | Zbl 0825.76607

[12] A. Karageorghis, A fully conforming spectral collocation scheme for second and fourth order problems. Comput. Methods Appl. Mech. Engng. 126 (1995) 305-314. | MR 1360098 | Zbl 0945.65522

[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. | MR 1089547 | Zbl 0709.76039

[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. | MR 1408535 | Zbl 0892.76064

[15] Z.-M. Lou, B. Bialecki, and G. Fairweather, Orthogonal spline collocation methods for biharmonic problems. Numer. Math. 80 (1998) 267-303. | MR 1645045 | Zbl 0908.65103

[16] W. W. Schuitz, N. Y. Lee and J. P. Boyd, Chebyshev pseudospectral method of viscous flows with corner singularities. J. Sci. Comput. 4 (1989) 1-19. | Zbl 0679.76042

[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. | MR 1298626 | Zbl 0811.65097