Journal of Scientific Computing

, Volume 6, Issue 4, pp 345–390

Spectral methods on triangles and other domains

  • Moshe Dubiner

DOI: 10.1007/BF01060030

Cite this article as:
Dubiner, M. J Sci Comput (1991) 6: 345. doi:10.1007/BF01060030


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 methodspectral elementstrianglewarped productresolutionpipe flowfast Fourier transform

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

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