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 GaussLegendre 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. © 2011 Elsevier B.V. All rights reserved.
Elliott, D., Johnston, P. R., & Johnston, B. M. (2011). Estimates of the error in GaussLegendre quadrature for double integrals. Journal of Computational and Applied Mathematics, 236(6), 1552–1561. https://doi.org/10.1016/j.cam.2011.09.019