Single and multi-interval legendre τ-methods in time for parabolic equations

Advances in Computational Mathematics

Volumn 17, Issue 4, 2002, Pages 349-367

  Tang, Jian Guo ^a,b   Ma, He Ping ^a  

^a SHANGHAI UNIVERSITY   (China)

^b Lingling College   (China)

Author keywords

Interval decomposition; Optimal error estimate; Parabolic equation; Spectral method in time

Indexed keywords

EID: 0141849406     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1016273820035     Document Type: Article

References (22)

1. I. Babuška and T. Janik, The h-p version of the finite element method for parabolic equations, part I: The p-version in time, Numer. Methods Partial Differential Equations 5 (1989) 363-399.
2. P. Bar-Yoseph, E. Moses, U. Zrahia and A.L. Yarin, Space-time spectral element methods for one-dimensional nonlinear advection-diffusion problems, J. Comput. Phys. 119 (1995) 62-74.
3. P.Z. Bar-Yoseph, Time finite element methods for initial value problems, Appl. Numer. Math. 33 (2000) 435-445.
4. C. Bernardi and Y. Maday, Spectral methods, in: Handbook of Numerical Analysis, Vol. 5, Techniques of Scientific Computing (Part 2), eds. EG. Ciarlet and J.L. Lions (Elsevier, Amsterdam, 1997) pp. 209-486.
5. C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, Spectral Methods in Fluid Dynamics (Springer, Berlin, 1988).
6. E.A. Coutsias, T. Hagstrom, J.S. Hesthaven and D. Torres, Integration preconditioners for differential operators in spectral tau-methods, in: Proc. of the 3rd Internat. Conf. on Spectral and High Order Methods, eds. A.V. Ilin and L.R. Scott (1996) pp. 21-38.
7. P. Gervasio and F. Saleri, Stabilized spectral element approximation for the Navier-Stokes equations, Numer. Methods Partial Differential Equations 14 (1998) 115-141.
8. I. Glenn, S. Brian and W. Rodney, Spectral methods in time for a class of parabolic partial differential equations, J. Comput. Phys. 102 (1992) 88-97.
9. B.-Y. Guo, Spectral Methods and Their Applications (World Scientific, Singapore, 1998).
10. J. Li, H.-P. Ma and W.-W. Sun, Error analysis for solving the Korteweg-de Vries equation by a Legendre pseudo-spectral method, Numer. Methods Partial Differential Equations 16 (2000) 513-534.
11. Y. Luo, Polynomial time-marching for three-dimensional wave equations, J. Sci. Comput. 12 (1997) 465-477.
12. Y. Luo and M.J. Yedlin, Polynomial time-marching for nonperiodic boundary value problems, J. Sci. Comput. 9 (1994) 123-136.
13. Y. Luo and M.J. Yedlin, Polynomial time-marching for nonreflecting boundary problems, J. Sci. Comput. 12 (1997) 31-50.
14. H.-P. Ma and W.-W. Sun, A Legendre Petrov-Galerkin and Chebyshev collocation method for third-order differential equations, SIAM J. Numer. Anal. 38 (2000) 1425-1438.
15. J. Shen, Efficient spectral-Galerkin method I. Direct solvers of second- and fourth-order equations using Legendre polynomials, SIAM J. Sci. Comput. 15 (1994) 1489-1505.
16. J. Shen, Efficient spectral-Galerkin method 11. Direct solvers of second- and fourth-order equations using Chebyshev polynomials, SIAM J. Sci. Comput. 16 (1995) 74-87.
17. H. Tal-Ezer, Spectral methods in time for hyperbolic problems, SIAM J. Numer. Anal. 23 (1986) 11-26.
18. H. Tal-Ezer, Spectral methods in time for parabolic problems, SIAM J. Numer. Anal. 26 (1989) 1-11.
19. S.-C. Wu and X.-Q. Liu, Spectral method in time for KdV equations, Appl. Math. Mech. (English ed.) 17 (1996) 357-362.
20. S.-C. Wu and X.-Q. Liu, Convergence of spectral method in time for Burgers' equation, Acta Math. Appl. Sinica (English ser.) 13 (1997) 314-320.
21. F.-Y. Zhang, Spectral and pseudo-spectral approximations in time for parabolic equations, J. Comput. Math. 16 (1998) 107-120.
22. U. Zrahia and P. Bar-Yoseph, Space-time spectral element method for solution of second-order hyperbolic equations, Comput. Methods Appl. Mech. Engrg. 116 (1994) 135-146.