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Spectral methods on triangles and other domains. (English) Zbl 0742.76059
Summary: 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.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D05 Navier-Stokes equations for incompressible viscous fluids
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
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References:
[1] Orszag, S. (1974). Fourier series on spheres,Mon. Weather Rev. 102(1), 56-75.
[2] Orszag, S., Israeli, M., and Deville, O. (1986). Boundary conditions for incompressible flows,J. Sci. Comput. 1(1), 75-111. · Zbl 0648.76023
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