## Error estimates in the numerical evaluation of some BEM singular integrals

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- by G. Mastroianni and G. Monegato;
- Math. Comp.
**70**(2001), 251-267 - DOI: https://doi.org/10.1090/S0025-5718-00-01272-2
- Published electronically: June 12, 2000
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## Abstract:

In some applications of Galerkin boundary element methods one has to compute integrals which, after proper normalization, are of the form \begin{equation*}\int _{a}^{b}\int _{-1}^{1}\frac {f(x,y)}{{x-y}}dxdy,\end{equation*} where $(a,b)\equiv (-1,1)$, or $(a,b)\equiv (a,-1)$, or $(a,b)\equiv (1,b)$, and $f(x,y)$ is a smooth function. In this paper we derive error estimates for a numerical approach recently proposed to evaluate the above integral when a $p-$, or $h-p$, formulation of a Galerkin method is used. This approach suggests approximating the inner integral by a quadrature formula of interpolatory type that exactly integrates the Cauchy kernel, and the outer integral by a rule which takes into account the $\log$ endpoint singularities of its integrand. Some numerical examples are also given.## References

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## Bibliographic Information

**G. Mastroianni**- Affiliation: Dipartimento di Matematica, Università della Basilicata, I-85100 Potenza, Italy
- Email: mg039sci@unibas.it
**G. Monegato**- Affiliation: Dipartimento di Matematica, Politecnico di Torino, I-10129 Torino, Italy
- Email: Monegato@polito.it
- Received by editor(s): February 17, 1999
- Published electronically: June 12, 2000
- Additional Notes: Work supported by the Consiglio Nazionale delle Ricerche - Comitato Nazionale per le Ricerche Tecnologiche e l’Innovazione, under contract n.96.01875.CT11.
- © Copyright 2000 American Mathematical Society
- Journal: Math. Comp.
**70**(2001), 251-267 - MSC (2000): Primary 41A55; Secondary 65D32, 65N38
- DOI: https://doi.org/10.1090/S0025-5718-00-01272-2
- MathSciNet review: 1803127