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.
Sang Dong Kim, Peyman Hessari, and Byeong-Chun Shin
Kyungpook National University, Kyungpook National University, Chonnam National University
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
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