Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Spectral and pseudospectral methods for advection equations

Author: Joseph E. Pasciak
Journal: Math. Comp. 35 (1980), 1081-1092
MSC: Primary 65M10; Secondary 65M15
MathSciNet review: 583488
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Spectral and pseudo spectral methods for advection equations are investigated. A basic framework is given which allows the application of techniques used in finite element analysis to spectral methods with trigonometric polynomials. Error estimates for semidiscrete spectral and pseudo spectral as well as fully discrete explicit pseudo spectral methods are given. The approximation schemes are shown to converge with infinite order.

References [Enhancements On Off] (What's this?)

  • [1] G. A. BAKER, J. H. BRAMBLE &. V. THOMÉE, "Single step Galerkin approximation for parabolic problems," Math. Comp., v. 31, 1977, pp. 818-847. MR 0448947 (56:7252)
  • [2] J. H. BRAMBLE, A. H. SCHATZ, V. THOMÉE & L. B. WAHLBIN, "Some convergence estimates for semidiscrete Galerkin type approximations for parabolic equations," SIAM J. Numer. Anal., v. 14, 1977, pp. 218-241. MR 0448926 (56:7231)
  • [3] P. L. BUTZER & R. J. NESSEL, Fourier Analysis and Approximation, Vol. 1, Academic Press, New York, 1971, p. 97. MR 0510857 (58:23312)
  • [4] O. CHRISTENSEN & L. PRAHM, "A pseudo spectral model for dispersion of atmospheric pollutants," J. Appl. Meteor., v. 15, 1976, pp. 1284-1294.
  • [5] B. FORNBERG, "On a Fourier method for the integration of hyperbolic equations," SIAM J. Numer. Anal., v. 12, 1975, pp. 509-528. MR 0421096 (54:9101)
  • [6] J. GAZDAG, "Numerical convective schemes based on accurate computation of space derivatives," J. Comput. Phys., v. 13, 1973, pp. 100-113.
  • [7] D. GOTTLIEB & S. ORSZAG, Numerical Analysis of Spectral Methods, SIAM-CBMS-NSF Conference Series, 1977, pp. 121-138.
  • [8] S. G. KREIN & Y. I. PETUNIN, "Scales of Banach spaces", Russian Math. Surveys, v. 21, 1966, pp. 85-160. MR 0193499 (33:1719)
  • [9] H. KREISS & J. OLIGER, "Stability of the Fourier method," SIAM J. Numer. Anal., v. 16, 1979, pp. 421-433. MR 530479 (80i:65130)
  • [10] A. MAJDA, J. McDONOUGH & S. OSHER, "The Fourier method for nonsmooth initial data," Math. Comp., v. 32, 1978, pp. 1041-1081. MR 501995 (80a:65197)
  • [11] S. ORZAG, "Comparison of pseudospectral and spectral approximations," Stud. Appl. Math., v. 51, 1972, pp. 253-259.
  • [12] M. TAYLOR, Pseudo Differential Operators, Springer-Verlag, Berlin and New York, 1974, pp. 62-65. MR 0442523 (56:905)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65M10, 65M15

Retrieve articles in all journals with MSC: 65M10, 65M15

Additional Information

Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society