Journal of Scientific Computing

, Volume 6, Issue 4, pp 345–390 | Cite as

Spectral methods on triangles and other domains

  • Moshe Dubiner
Article

Abstract

This article shows how to obtain multidimensional spectral methods as a warped product of one-dimensional spectral methods, thus generalizing direct (tensor) products. This generalization includes the fast Fourier transform. Applications are given for spectral approximation on a disk and on a triangle. The use of the disk spectral method for simulating the Navier-Stokes equations in a periodic pipe is detailed. The use of the triangle method in a spectral element scheme is discussed. The degree of approximation of the triangle method is computed in a new way, which favorably compares with the classical approximation estimates.

Key words

Spectral method spectral elements triangle warped product resolution pipe flow fast Fourier transform 

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References

  1. Orszag, S. (1974). Fourier series on spheres,Mon. Weather Rev. 102(1), 56–75.Google Scholar
  2. Orszag, S., Israeli, M., and Deville, O. (1986). Boundary conditions for incompressible flows,J. Sci. Comput. 1(1), 75–111.Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • Moshe Dubiner
    • 1
  1. 1.Department of Applied MathematicsTel-Aviv UniversityRamat-AvivIsrael

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