Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2014; 51(2): 595-612

Printed March 31, 2014

https://doi.org/10.4134/BKMS.2014.51.2.595

Copyright © The Korean Mathematical Society.

Preconditioned spectral collocation method on curved element domains using the Gordon-Hall transformation

Sang Dong Kim, Peyman Hessari, and Byeong-Chun Shin

Kyungpook National University, Kyungpook National University, Chonnam National University

Abstract

The spectral collocation method for a second order elliptic boundary value problem on a domain $\Omega$ with curved boundaries is studied using the Gordon and Hall transformation which enables us to have a transformed elliptic problem and a square domain $S = [0,h]\times[0,h]$, $h>0$. The preconditioned system of the spectral collocation approximation based on Legendre-Gauss-Lobatto points by the matrix based on piecewise bilinear finite element discretizations is shown to have the high order accuracy of convergence and the efficiency of the finite element preconditioner.

Keywords: spectral collocation method, Gordon and Hall transformation, elliptic equation

MSC numbers: Primary 65F10, 65F30