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Tensor product Gauss-Lobatto points are Fekete points for the cube

Authors: L. Bos, M. A. Taylor and B. A. Wingate
Journal: Math. Comp. 70 (2001), 1543-1547
MSC (2000): Primary 41A10, 65D32, 65M60, 65M70
Published electronically: April 19, 2000
MathSciNet review: 1836917
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Abstract | References | Similar Articles | Additional Information


Tensor products of Gauss-Lobatto quadrature points are frequently used as collocation points in spectral element methods. Unfortunately, it is not known if Gauss-Lobatto points exist in non-tensor-product domains like the simplex. In this work, we show that the $n$-dimensional tensor-product of Gauss-Lobatto quadrature points are also Fekete points. This suggests a way to generalize spectral methods based on Gauss-Lobatto points to non-tensor-product domains, since Fekete points are known to exist and have been computed in the triangle and tetrahedron. In one dimension this result was proved by Fejér in 1932, but the extension to higher dimensions in non-trivial.

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Additional Information

L. Bos
Affiliation: Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta Canada

M. A. Taylor
Affiliation: Los Alamos National Laboratory, Los Alamos, New Mexico

B. A. Wingate
Affiliation: Los Alamos National Laboratory, Los Alamos, New Mexico

Keywords: Fekete Gauss Lobatto quadrature, spectral element methods
Received by editor(s): November 10, 1999
Published electronically: April 19, 2000
Article copyright: © Copyright 2000 American Mathematical Society