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29-04-2015 | Issue 2/2016

Journal of Scientific Computing 2/2016

Spectral Method for Fourth-Order Problems on Quadrilaterals

Journal:
Journal of Scientific Computing > Issue 2/2016
Authors:
Xu-hong Yu, Ben-yu Guo
Important notes
This work is supported in part by NSF of China N.11171227 and N.11426155, Fund for Doctoral Authority of China N.20123127110001, Fund for E-institute of Shanghai Universities N.E03004, Leading Academic Discipline Project of Shanghai Municipal Education Commission N.J50101, and the Hujiang Foundation of China (B14005).

Abstract

In this paper, we investigate the spectral method for fourth-order problems defined on quadrilaterals. Some results on the Legendre irrational orthogonal approximations are established, which play important roles in the related spectral method on quadrilaterals. As examples of applications, we provide spectral schemes for a model problem with various boundary conditions. The spectral accuracy of suggested algorithms are proved. Numerical results demonstrate the effectiveness of suggested algorithms, and confirm the analysis well. The approximation results and techniques developed in this paper are also applicable to other fourth-order problems defined on quadrilaterals.

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