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ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis, pp. 541-588, 2024/11/18
This paper deals with a new boundary integral equation method for the numerical solution of the exterior Neumann problem for the Laplace equation in planar domains with corners. Using the single layer representation of the potential, the differential problem is reformulated in terms of a boundary integral equation (BIE) whose solution has singularities at the corners. A “modified” Nyström-type method based on a Gauss–Jacobi–Lobatto quadrature formula is proposed for its approximation. Convergence and stability results are proved in proper weighted spaces of continuous functions. Moreover, the use of a smoothing transformation allows one to increase the regularity of the solution and, consequently, the order of convergence of the method. The efficiency of the proposed method is illustrated by some numerical tests.
Keywords: boundary integral equations, Neumann problem, domains with corners, Nyström method