TITLE:
Finite Difference Preconditioners for Legendre Based Spectral Element Methods on Elliptic Boundary Value Problems
AUTHORS:
Seonhee Kim, Amik St-Cyr, Sang Dong Kim
KEYWORDS:
Finite Difference Preconditioner; Iterative Method; Spectral Element Method; Elliptic Operator
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.5,
May
22,
2013
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.