On quadrature methods for the double layer potential equation over the boundary of a polyhedron
type: Item
instance of: scholarly article
title: On quadrature methods for the double layer potential equation over the boundary of a polyhedron
zbMATH Open document ID: 0791.65088
DOI: 10.1007/BF01385688
published in: Numerische Mathematik
publication date: 1994-07-07T00:00:00Z
full work available at URL: https://eudml.org/doc/133753
review text: We consider a quadrature method for the solution of the double layer potential equation corresponding to the Laplace equation in a three- dimensional polyhedron. We prove the stability for our method in case of special triangulations over the boundary of the polyhedron. The assumptions imposed on the triangulations are analogous to those appearing in the one-dimensional case. Finally, we establish the rates of convergence and discuss the effect of mesh refinement near the corners and edges of the polyhedron.
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35C15
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 569149
zbMATH Keywords: boundary integral equation method
zbMATH Keywords: quadrature method
zbMATH Keywords: double layer potential equation
zbMATH Keywords: Laplace equation
zbMATH Keywords: stability
zbMATH Keywords: triangulations
zbMATH Keywords: convergence
zbMATH Keywords: mesh refinement
author: Andreas Rathsfeld
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 569149