The optimal rate of convergence of the \(p\)-version of the boundary element method in two dimensions
type: Item
instance of: scholarly article
title: The optimal rate of convergence of the \(p\)-version of the boundary element method in two dimensions
zbMATH Open document ID: 1060.65117
published in: Numerische Mathematik
publication date: 2005-01-19T00:00:00Z
review text: The authors formulate two theorems concerning the optimal convergence of the \(p\)-version of the boundary element solution to the boundary integral equations of the first kind corresponding to Dirichlet and Neumann problems for Laplace's equation. In order to prove these results they introduce some elements of the approximation theory such as the approximability of functions in the Jacobi-weighted Besov and Sobolev spaces.
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65N15
zbMATH DE Number: 2130176
zbMATH Keywords: Laplace's equation
zbMATH Keywords: Dirichlet and Neumann problems
zbMATH Keywords: boundary element method
zbMATH Keywords: p-version
zbMATH Keywords: hypersingular operators
zbMATH Keywords: weakly singular integral operators
zbMATH Keywords: 2D polygonal domains
zbMATH Keywords: energy norms
zbMATH Keywords: convergence
zbMATH Keywords: boundary integral equations
zbMATH Keywords: Besov space
zbMATH Keywords: Sobolev space
author: Benqi Guo
author: Norbert Heuer
reviewed by: Calin Ioan Gheorghiu
MaRDI profile type: Publication
full work available at URL: s00211-004-0535-8
OpenAlex ID: W2108087611
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DOI: 10.1007/S00211-004-0535-8
description: scientific article; zbMATH DE number 2130176