High order convergence for collocation of second kind boundary integral equations on polygons
type: Item
instance of: scholarly article
title: High order convergence for collocation of second kind boundary integral equations on polygons
zbMATH Open document ID: 0897.65073
author: Pascal Laubin
published in: Numerische Mathematik
publication date: 1998-10-05T00:00:00Z
review text: The paper deals with the double layer potential \(Ku\) (\(u\) being the density), defined as the surface integral over the connected polygonal boundary of a bounded domain in \(\mathbb{R}^2\). Theorem 1 claims that \(K\) is an isomorphism between some spaces of Sobolev type. For solving the equation \(Ku= f\) approximately a system of collocation equations is proposed and estimates of the error are given in Theorems 2, 3. The proofs of the theorems are based on some properties of the Mellin transform, which is studied thoroughly in the paper and on a suitable extension of Cea's lemma. Numerical experiments are also presented.
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65N12
zbMATH DE Number: 1145974
zbMATH Keywords: boundary integral equations
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: numerical experiments
zbMATH Keywords: double layer potential
zbMATH Keywords: Mellin transform
zbMATH Keywords: Cea's lemma
reviewed by: Hanna Marcinkowska
MaRDI profile type: Publication
full work available at URL: s002110050333
OpenAlex ID: W2059563756
DOI: 10.1007/S002110050333
description: scientific article; zbMATH DE number 1145974