Preconditioning on high-order element methods using Chebyshev--Gauss--Lobatto nodes

Authors:
Seonhee Kim;Sang Dong Kim
Affiliations:
Department of Mathematics, Kyungpook National University, Daegu 702-701, Korea;Department of Mathematics, Kyungpook National University, Daegu 702-701, Korea
Venue:
Applied Numerical Mathematics
Year:
2009

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Abstract

Based on Chebyshev-Gauss-Lobatto points, the piecewise linear finite element preconditioner is analyzed in terms of condition numbers for the high-order element discretizations applied to a model elliptic operator. The optimality of such a preconditioner is proved for one-dimensional case and the scalability is shown for two-dimensional case. Further, we provide O(N^1^/^3) growth of piecewise linear finite element preconditioner numerically.