• Ronny Ramlau, Lothar Reichel (Hg.)

ETNA - Electronic Transactions on Numerical Analysis

Bild


Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.

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

Bestellung/Order


Bild
ETNA - Electronic Transactions on Numerical Analysis



ISBN 978-3-7001-8258-0
Online Edition



Send or fax to your local bookseller or to:

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: bestellung.verlag@oeaw.ac.at
UID-Nr.: ATU 16251605, FN 71839x Handelsgericht Wien, DVR: 0096385

Bitte senden Sie mir
Please send me
 
Exemplar(e) der genannten Publikation
copy(ies) of the publication overleaf


NAME


ADRESSE / ADDRESS


ORT / CITY


LAND / COUNTRY


ZAHLUNGSMETHODE / METHOD OF PAYMENT
    Visa     Euro / Master     American Express


NUMMER

Ablaufdatum / Expiry date:  

    I will send a cheque           Vorausrechnung / Send me a proforma invoice
 
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)
Bild

A stable BIE method for the Laplace equation with Neumann boundary conditions in domains with piecewise smooth boundaries

    Peter Junghanns, Concetta Laurita

ETNA - Electronic Transactions on Numerical Analysis, pp. 541-588, 2024/11/18

doi: 10.1553/etna_vol60s541

doi: 10.1553/etna_vol60s541


PDF
X
BibTEX-Export:

X
EndNote/Zotero-Export:

X
RIS-Export:

X 
Researchgate-Export (COinS)

Permanent QR-Code

doi:10.1553/etna_vol60s541



doi:10.1553/etna_vol60s541

Abstract

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