Finite Difference Preconditioners for Legendre Based Spectral Element Methods on Elliptic Boundary Value Problems

Seonhee Kim, Amik St-Cyr, Sang Dong Kim

Computation and Modeling, Shell Technology Center Houston (STCH), Houston, USA.
Department of Mathematics, Kyungpook National University, Daegu, South Korea.

DOI: 10.4236/am.2013.45115                

Abstract

Finite difference type preconditioners for spectral element discretizations based on Legendre-Gauss-Lobatto points are analyzed. The latter is employed for the approximation of uniformly elliptic partial differential problems. In this work, it is shown that the condition number of the resulting preconditioned system is bounded independently of both of the polynomial degrees used in the spectral element method and the element sizes. Several numerical tests verify the h-p independence of the proposed preconditioning.

Keywords

Finite Difference Preconditioner; Iterative Method; Spectral Element Method; Elliptic Operator

Conflicts of Interest

The authors declare no conflicts of interest.

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