ISSN:
0945-3245
Keywords:
Mathematics Subject Classification (1991): 65R20, 65N38, 65N35, 65R30, 65N12
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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 $L_n$ (where $n$ denotes the division number) are investigated. We show that the maximum norm of $L^{-1}_n$ and the condition number of $L_n$ have the forms: $C_0 n + O (1)$ and $C_1 n +o (n)$ , respectively, as $n \to \infty$ , where the constants $C_0$ and $C_1$ are explicitly given in the proof. Although these estimates indicate illconditionedness of this numerical computation, the $O(n^{-2})$ -convergence of this scheme with maximum norm is proved as an application of the main results.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002110050191
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