Asymptotic estimation for the condition numbers in
BEM |
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Authors: | Masato Kimura |
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Institution: | (1) Osaka Kyoiku University, Asahigaoka 4-698-1, Kashiwara, 582, Japan; e-mail: masato@cc.osaka-kyoiku.ac.jp , JP |
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Abstract: | Summary.
We apply the boundary element methods (BEM) to the interior Dirichlet problem of the
two dimensional Laplace equation, and its discretization is carried out
with the collocation method using piecewise linear elements. In this paper,
some precise asymptotic estimations for the discretization matrix
(where denotes
the division number) are investigated. We show that the maximum norm of
and the condition number of
have the forms:
and , respectively, as
, where the constants
and are explicitly given in
the proof. Although these estimates
indicate illconditionedness of this numerical computation,
the -convergence
of this scheme with maximum norm is
proved as an application of the main
results.
Received
January 25, 1993 / Revised version received March 13,
1995 |
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Keywords: | Mathematics Subject Classification (1991): 65R20 65N38 65N35 65R30 65N12 |
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