Semi-discrete Galerkin approximations for the single-layer equation on Lipschitz curves
type: Item
instance of: scholarly article
title: Semi-discrete Galerkin approximations for the single-layer equation on Lipschitz curves
zbMATH Open document ID: 0899.65067
author: Ian H. Sloan
author: Kendall E. Atkinson
published in: Journal of Integral Equations and Applications
publication date: 1998-10-27T00:00:00Z
full work available at URL: cont9-3.htm
review text: This paper provides a stability and error analysis for a class of Galerkin methods for the single-layer equation on piecewise-smooth curves in the plane. These Galerkin methods use piecewise-constant basis functions, but the mesh on the boundary curve need not be uniform. The only requirement is that the quadrature method used to approximate the Galerkin integrals be sufficiently exact, either by the choice of a fine enough grid or by the use of a proper quadrature order.
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 1156428
zbMATH Keywords: singular integral equation
zbMATH Keywords: Lipschitz curves
zbMATH Keywords: collocation
zbMATH Keywords: integral equation method
zbMATH Keywords: stability
zbMATH Keywords: error analysis
zbMATH Keywords: Galerkin methods
zbMATH Keywords: single-layer equation
zbMATH Keywords: quadrature method
reviewed by: Gerald W. Hedstrom
MaRDI profile type: Publication
OpenAlex ID: W2025155618
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DOI: 10.1216/JIEA/1181076016
description: scientific article; zbMATH DE number 1156428