Journal of Scientific Computing

, Volume 6, Issue 4, pp 345-390

First online:

Spectral methods on triangles and other domains

  • Moshe DubinerAffiliated withDepartment of Applied Mathematics, Tel-Aviv University

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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