Pseudospectral method for quadrilaterals

Authors:
Ben-yu Guo;Hong-li Jia
Affiliations:
Department of Mathematics, Shanghai Normal University, 200234, Shanghai, China and Scientific Computing Key Laboratory of Shanghai Universities, Division of Computational Science of E-institute of ...;Department of Mathematics, Shanghai Normal University, 200234, Shanghai, China and Department of Mathematics, Donghua University, 200065, Shanghai, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

In this paper, we investigate the pseudospectral method on quadrilaterals. Some results on Legendre-Gauss-type interpolation are established, which play important roles in the pseudospectral method for partial differential equations defined on quadrilaterals. As examples of applications, we propose pseudospectral methods for two model problems and prove their spectral accuracy in space. Numerical results demonstrate the efficiency of the suggested algorithms. The approximation results and techniques developed in this paper are also applicable to other problems defined on quadrilaterals.