Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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PRECONDITIONED SPECTRAL COLLOCATION METHOD ON CURVED ELEMENT DOMAINS USING THE GORDON-HALL TRANSFORMATION

  • Kim, Sang Dong (Department of Mathematics Kyungpook National University) ;
  • Hessari, Peyman (Institute of Mechanical Engineering Technology Kyungpook National University) ;
  • Shin, Byeong-Chun (Department of Mathematics Chonnam National University)
  • Received : 2013.01.16
  • Published : 2014.03.31
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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.

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References

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