Free access
Issue
ESAIM: M2AN
Volume 41, Number 6, November-December 2007
Page(s) 1021 - 1039
DOI http://dx.doi.org/10.1051/m2an:2007052
Published online 15 December 2007
  1. C. Canuto and P. Pietra, Boundary interface conditions within a finite element preconditioner for spectral methods. J. Comput. Phys. 91 (1990) 310–343. [CrossRef] [MathSciNet]
  2. C. Canuto and A. Quarteroni, Spectral and pseudo-spectral methods for parabolic problems with nonperiodic boundary conditions. Calcolo 18 (1981) 197–218. [CrossRef] [MathSciNet]
  3. C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, Spectral Methods in Fluid Dynamics. Springer, New York (1988).
  4. L. Fatone, D. Funaro and G.J. Yoon, A convergence analysis for the superconsistent Chebyshev method. Appl. Num. Math. (2007) (to appear).
  5. D. Funaro, Polynomial Approximation of Differential Equations, Lecture Notes in Physics 8. Springer, Heidelberg (1992).
  6. D. Funaro, Some remarks about the collocation method on a modified Legendre grid. J. Comput. Appl. Math. 33 (1997) 95–103.
  7. D. Funaro, Spectral Elements for Transport-Dominated Equations, Lecture Notes in Computational Science and Engineering 1. Springer (1997).
  8. D. Funaro, A superconsistent Chebyshev collocation method for second-order differential operators. Numer. Algorithms 28 (2001) 151–157. [CrossRef] [MathSciNet]
  9. D. Funaro, Superconsistent discretizations. J. Scientific Computing 17 (2002) 67–80. [CrossRef]
  10. D. Gottlieb, M.Y. Hussaini and S.A. Orszag, Theory and application of spectral methods, in Spectral Methods for Partial Differential Equations, R.G. Voigt, D. Gottlieb and M.Y. Hussaini Eds., SIAM, Philadelphia (1984).
  11. P. Haldenwang, G. Labrosse, S. Abboudi and M. Deville, Chebyshev 3-D spectral and 2-D pseudospectral solvers for the Helhmoltz equation. J. Comput. Phys. 55 (1981) 115–128. [CrossRef]
  12. T. Kilgore, A characterization of the Lagrange interpolation projections with minimal Tchebycheff norm. J. Approximation Theory 24 (1978) 273–288. [CrossRef]
  13. D.H. Kim, K.H. Kwon, F. Marcellán and S.B. Park, On Fourier series of a discrete Jacobi-Sobolev inner product. J. Approximation Theory 117 (2002) 1–22. [CrossRef]
  14. S.D. Kim and S.V. Parter, Preconditioning Chebyshev spectral collocation method for elliptic partial differential equations. SIAM J. Numer. Anal. 33 (1996) 2375–2400. [CrossRef] [MathSciNet]
  15. S.D. Kim and S.V. Parter, Preconditioning Chebyshev spectral collocation by finite-difference operators. SIAM J. Numer. Anal. 34 (1997) 939–958. [CrossRef] [MathSciNet]
  16. F. Marcellán, B.P. Osilenker and I.A. Rocha, Sobolev-type orthogonal polynomials and their zeros. Rendiconti di Matematica 17 (1997) 423–444.
  17. E.H. Mund, A short survey on preconditioning techniques in spectral calculations. Appl. Num. Math. 33 (2000) 61–70. [CrossRef]
  18. S.A. Orszag, Spectral methods for problems in complex geometries. J. Comput. Phys. 37 (1980) 70–92. [CrossRef] [MathSciNet]
  19. G. Szegö, Orthogonal Polynomials. American Mathematical Society, New York (1939).
  20. L.N. Trefethen and M. Embree, Spectra and Pseudospectra: the behavior of nonnormal matrices and operators. Princeton University Press (2005).

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