Exponential convergence of the \(hp\)-version for the boundary element method on open surfaces
type: Item
instance of: scholarly article
title: Exponential convergence of the \(hp\)-version for the boundary element method on open surfaces
zbMATH Open document ID: 0946.65120
author: Norbert Heuer
author: Matthias Maischak
author: Ernst P. Stephan
published in: Numerische Mathematik
publication date: 2000-10-10T00:00:00Z
review text: The authors study the \(hp\)-version of the Galerkin boundary element method applied to weakly singular and hypersingular integral equations of the first kind on open surfaces with piecewise smooth boundary. They prove exponential convergence for both integral equations if geometrically refined meshes are used. The proof is based on the special structure of the singularities at the corners and edges, which can be efficiently approximated by piecewise tensor products of splines of different degree.
reviewed by: Gunther Schmidt
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65N12
zbMATH DE Number: 1398757
zbMATH Keywords: Galerkin boundary element method
zbMATH Keywords: weakly singular integral operator
zbMATH Keywords: hypersingular operator
zbMATH Keywords: open surface
zbMATH Keywords: piecewise smooth boundary
zbMATH Keywords: geometrically refined mesh
zbMATH Keywords: exponential convergence
zbMATH Keywords: tensor products of splines
MaRDI profile type: Publication
full work available at URL: s002119900082
OpenAlex ID: W2035409961
DOI: 10.1007/S002119900082
description: scientific article; zbMATH DE number 1398757