Abstract
An approximation of the double layer logarithmic potential is obtained as a solution to a discrete Laplacian equation with a new right-hand side. The error is estimated under the assumption that the potential belongs to some Besov spaces. Since the right hand side includes evaluation of line integrals, we use appropriate quadratures for their computation. The well know scheme of A. Mayo, 1984, can be obtained as a partial case.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
Friedman, A.: Mathematics in industrial problems. Springer (1992)
Gold J., Graham I.: Towards automatition of boundary integral methods for Laplace's equation. in ”Mathematics of finite elements and applications” Academic Press (1991) 349–360
Golovin G., Makarov M., Sablin M., Sukhachev D., Yakovlev V.: Comparison of various methods for solving the Dirichlet problem for the Laplace equation in complicated domains. Zh. Vychisl. Mat. Fiz. 27 (1987) 1662–1679 (in Russian)
Drenska, N.: Computation of potentials used in the boundary element method. Colloq. Math. Soc. Janos Bolyai 59 (1990) 157–163
Kolkovska, N.: Reconstruction of some potentials used in the boundary element method. J. of Integral Equations and Applications 5 (1993) 345–367
Kress, R.: Linear integral equations. Springer (1989) 298
Lazarov, R., Mokin Yu. On the computation of the logarithmic potential. Soviet Math. Dokl. 28 (1983) 320–323
Mayo A.: The fast solution of Poisson's and the biharmonic equation on irregular regions. SIAM J. Numer. Anal. 21 (1984) 285–299
Mayo A., Greenbaum A.: Fast parallel iterative solutions of Poisson's and the biharmonic equations on irregular domains. SIAM J. Sci. Stat. Comp. 13(1992) 101–118
Mokin, Yu.: Methods of calculating a logarithmic potential. Izd. Moskovsk. Gos. Univ., Moscow (1988) 124 (in Russian)
Yakovlev V. On the computation of the flaxere of the thin plate with leant edges Vestn. MGU, ser. 15 (1985) 19–22 (in Russian)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kolkovska, N. (1997). Numerical methods for computation of the double layer logarithmic potential. In: Vulkov, L., Waśniewski, J., Yalamov, P. (eds) Numerical Analysis and Its Applications. WNAA 1996. Lecture Notes in Computer Science, vol 1196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62598-4_100
Download citation
DOI: https://doi.org/10.1007/3-540-62598-4_100
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62598-8
Online ISBN: 978-3-540-68326-1
eBook Packages: Springer Book Archive