An enhanced pseudospectral Chebyshev method for dissipative partial differential equations

Journal of Computational and Applied Mathematics

Volumn 115, Issue 1-2, 2000, Pages 137-150

  De Frutos, Javier ^a   Novo, Julia ^a  

^a UNIVERSITY OF VALLADOLID   (Spain)

Author keywords

Aliasing errors; Chebyshev spectral and pseudospectral methods; Dissipative equation

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; FOURIER TRANSFORMS; GALERKIN METHODS; MATHEMATICAL OPERATORS; PARTIAL DIFFERENTIAL EQUATIONS; POLYNOMIALS;

ALIASING ERRORS; DISSIPATIVE EQUATIONS; POSTPROCESSING; PSEUDOSPECTRAL CHEBYSHEV METHOD;

CHEBYSHEV APPROXIMATION;

EID: 0034159007     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(99)00173-9     Document Type: Article

References (15)

1. Bernardi C., Maday Y. Properties of some weighted Sobolev spaces and application to spectral approximations. SIAM J. Numer. Anal. 26:1989;769-829.
2. C. Bernardi, Y. Maday, Approximations Spectrales de Problémes aux Limites Elliptiques, Springer, Paris, 1992.
3. C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods in Fluid Dynamics, Springer Series in Computational Mathematics, Springer, Berlin, 1998.
4. B. Fornberg, A Practical Guide to Pseudospectral Methods, Cambridge University Press, Cambridge, 1996.
5. J. de Frutos, J. Novo, A postprocess based improvement of the spectral element method, Appl. Numer. Math., to appear.
6. J. de Frutos, J. Novo, A spectral element method for the Navier-Stokes equations with improved accuracy, Applied Mathematics and Computation Reports, July 1998.
7. J. de Frutos, B. García-Archilla, J. Novo, A postprocessed Galerkin method with Chebyshev or Legendre polynomials, Applied Mathematics and Computation Reports, July 1996.
8. García-Archilla B., Novo J., Titi E. Postprocessing the Galerkin method: a novel approach to approximate inertial manifolds. SIAM J. Numer. Anal. 35:1998;941-972.
9. B. García-Archilla, J. Novo, E. Titi, An approximate inertial manifods approach to postprocessing the Galerkin method for the Navier-Stokes equations, Math. Comp., to appear.
10. J. Novo, Postproceso de métodos espectrales. Ph.D. Thesis, Universidad de Valladolid, 1997.
11. J. Novo, S. Wynne, E. Titi, Efficient methods using high accuracy approximate inertial manifolds, Numer. Math., to appear.
12. Shen J. Efficient spectral-Galerkin method II. Direct solvers of second and four order equations using Chebyshev polynomials. SIAM J. Sci. Comput. 16:1995;74-87.
13. Shen J., Temam R. Nonlinear Galerkin method using Chebyshev and Legendre polynomials I. The one-dimensional case. SIAM J. Numer. Anal. 32:1995;215-234.
14. Tadmor E. The exponential accuracy of Fourier and Chebyshev differencing methods. SIAM J. Numer. Anal. 1:1986;1-10.
15. R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics, Applied Mathematical Sciences, Vol. 68, Springer, Berlin, 1988.