A spectral method on tetrahedra using rational basis functions
Huiyuan Li 1, Li-Lian Wang 21 Institute of Software, Chinese Academy of Sciences, Beijing 100190, China.
2 Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore.
Received by the editors May 31, 2009 and, in revised form, September 20, 2009.
A spectral method using fully tensorial rational basis functions on tetrahedron, obtained from the polynomials on the reference cube through a collapsed coordinate transform, is proposed and analyzed. Theoretical and numerical results show that the rational approximation is as accurate as the polynomial approximation, but with a more effective implementation.
AMS subject classifications: 65N35, 65N22, 65F05, 35J05
Key words: Spectral methods on tetrahedra, rational basis functions, spectral accuracy.
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