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A complete error analysis for the evaluation of a two-dimensional nearly singular boundary element integral

Citation

Elliott, D and Johnston, BM and Johnston, PR, A complete error analysis for the evaluation of a two-dimensional nearly singular boundary element integral, Journal of Computational and Applied Mathematics, 279 pp. 261-276. ISSN 0377-0427 (2015) [Refereed Article]

Copyright Statement

Copyright 2014 Published by Elsevier B.V.

DOI: doi:10.1016/j.cam.2014.11.015

Abstract

An important aspect of numerical integration is to have some knowledge of the truncation error for a given number of integration points. In this paper we determine estimates for these errors in the application of Gauss–Legendre quadrature to evaluate numerically two dimensional integrals which arise in the boundary element method. Expressions for the truncation errors developed here require the approximate evaluation of two integrals in the complex plane. The second integral, which has been termed the "remainder of the remainder", was assumed small by the authors in a previous attempt in developing error estimates. However, here this integral is included and it is evaluated using a novel approach for the choice of contour. We consider examples where ignoring the "remainder of the remainder" was a reasonable assumption and also consider cases where this remainder dominates the error. Finally, it is shown, for each of the integrals considered, that these new error estimates agree very closely with the actual quadrature error.

Item Details

Item Type:Refereed Article
Keywords:double integrals, Gauss-Legendre quadrature, numerical integration, error estimates
Research Division:Mathematical Sciences
Research Group:Pure Mathematics
Research Field:Ordinary Differential Equations, Difference Equations and Dynamical Systems
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Elliott, D (Professor David Elliott)
ID Code:97346
Year Published:2015
Web of Science® Times Cited:1
Deposited By:Mathematics and Physics
Deposited On:2014-12-11
Last Modified:2017-11-01
Downloads:0

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