Preconditioned spectral collocation method on curved element domains using the Gordon-Hall transformation
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The spectral collocation method for a second order elliptic boundary value problem on a domain Ω with curved boundaries is stud- ied using the Gordon and Hall transformation which enables us to have a transformed elliptic problem and a square domain S = [0, h] × [0, h], h > 0. The preconditioned system of the spectral collocation approx- imation 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.
Abstract
The spectral collocation method for a second order elliptic boundary value problem on a domain Ω with curved boundaries is stud- ied using the Gordon and Hall transformation which enables us to have a transformed elliptic problem and a square domain S = [0, h] × [0, h], h > 0. The preconditioned system of the spectral collocation approx- imation 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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