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Int. J. Numer. Anal. Mod., 7 (2010), pp. 330-355. |
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A spectral method on tetrahedra using rational basis functions Huiyuan Li 1, Li-Lian Wang 2 1 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. Abstract
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. Email: lihuiyuan@gmail.com, lilian@ntu.edu.sg |