Estimates of the error in Gauss-Legendre quadrature for double integrals

Authors:
David Elliott;Peter R. Johnston;Barbara M. Johnston
Affiliations:
School of Mathematics and Physics, University of Tasmania, Private Bag 37, GPO Hobart, Tasmania 7001, Australia;School of Biomolecular and Physical Sciences, Griffith University, Nathan, Queensland 4111, Australia;School of Biomolecular and Physical Sciences, Griffith University, Nathan, Queensland 4111, Australia
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

Error estimates are a very important aspect of numerical integration. It is desirable to know what level of truncation error might be expected for a given number of integration points. Here, we determine estimates for the truncation error when Gauss-Legendre quadrature is applied to the numerical evaluation of two dimensional integrals which arise in the boundary element method. Two examples are considered; one where the integrand contains poles, when its definition is extended into the complex plane, and another which contains branch points. In both cases we obtain error estimates which agree with the actual error to at least one significant digit.