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Spectral method on quadrilaterals

Authors: Guo Ben-yu and Jia Hong-li
Journal: Math. Comp. 79 (2010), 2237-2264
MSC (2010): Primary 65N35, 41A30, 35J05
Published electronically: April 8, 2010
MathSciNet review: 2684363
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Abstract: In this paper, we investigate the spectral method on quadrilaterals. We introduce an orthogonal family of functions induced by Legendre polynomials, and establish some results on the corresponding orthogonal approximation. These results play important roles in the spectral method for partial differential equations defined on quadrilaterals. As examples of applications, we provide spectral schemes for two model problems and prove their spectral accuracy in Jacobi weighted Sobolev space. Numerical results coincide well with the analysis. We also investigate the spectral method on convex polygons whose solutions possess spectral accuracy. The approximation results of this paper are also applicable to other problems.

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Additional Information

Guo Ben-yu
Affiliation: Department of Mathematics, Shanghai Normal University, 200234, Shanghai, People’s Republic of China

Jia Hong-li
Affiliation: Department of Mathematics, Donghua University, 200065, Shanghai, People’s Republic of China

Keywords: Orthogonal approximation on quadrilaterals, spectral method.
Received by editor(s): July 15, 2008
Received by editor(s) in revised form: April 30, 2009, and June 21, 2009
Published electronically: April 8, 2010
Additional Notes: The work of this author is supported in part by NSF of China N.10871131, Science and Technology Commission of Shanghai Municipality, Grant N.075105118, Shanghai Leading Academic Discipline Project N.S30405, and Fund for E-institute of Shanghai Universities N.E03004.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.