On the essential norm of the double layer potential on polyhedral domains and the stability of the collocation method
type: Item
instance of: scholarly article
title: On the essential norm of the double layer potential on polyhedral domains and the stability of the collocation method
zbMATH Open document ID: 1009.65073
author: Olaf Hansen
published in: Journal of Integral Equations and Applications
publication date: 2002-10-14T00:00:00Z
full work available at URL: CONT13-3.html
review text: The author studies the double layer operator on a polyhedral domain \(D\) in \({\mathbb R}^{3}\) and constructs weighted norms for a class of nonconvex cones, such that the double layer operator has a norm smaller than \(1/2\) with respect to this weighted norm. This allows to prove the stability for the collocation method with piecewise polynomial trial functions of arbitrary degree if some modifications near the vertices are introduced and if the grid respects the weighted norm in some given sense.
reviewed by: Ariadna Lucia Pletea
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65N12
zbMATH DE Number: 1779484
zbMATH Keywords: double layer potential
zbMATH Keywords: polyhedral domains
zbMATH Keywords: collocation method
zbMATH Keywords: stability
MaRDI profile type: Publication
OpenAlex ID: W2029178564
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DOI: 10.1216/JIEA/1020254673
description: scientific article; zbMATH DE number 1779484