Analytical integration of elliptic 2D fundamental solution and its derivatives for straight-line elements with constant interpolation
type: Item
instance of: scholarly article
title: Analytical integration of elliptic 2D fundamental solution and its derivatives for straight-line elements with constant interpolation
zbMATH Open document ID: 0940.65130
DOI: 10.1016/S0955-7997(98)00099-X
author: Z. Rek
author: B. Šarler
published in: Engineering Analysis with Boundary Elements
publication date: 2000-07-10T00:00:00Z
review text: The authors describe the analytical integration of the elliptic 2D fundamental solution and its 1st, 2nd and 3rd derivatives with the constant function interpolation for straight-line boundary elements. As a result of the character of the integrated function, the integrals are characterized with regard to the position of the source point. If it lies on the boundary \(\Gamma\), then the integrals are weak-(\(\log r\)), strong-(\(1/r\)) and hyper-(\(1/r^2\)) singular. Otherwise, the integrals are regular. A comparison of the analytical and the numerical integrations is made.
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 65D30
Mathematics Subject Classification ID: 65D25
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 1389988
zbMATH Keywords: boundary element method
zbMATH Keywords: numerical integration
zbMATH Keywords: fundamental solution
zbMATH Keywords: Laplace equation
zbMATH Keywords: straight-line elements
zbMATH Keywords: derivatives
reviewed by: Karel Najzar
MaRDI profile type: Publication
cites work: Q3219912
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full work available at URL: s0955-7997(98)00099-x
OpenAlex ID: W2015895886
description: scientific article; zbMATH DE number 1389988