June  2006, 5(2): 337-347. doi: 10.3934/cpaa.2006.5.337

Extrapolation expansions for Hanging-Chad-Type Galerkin integrals with plane triangular elements

1. 

Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439, United States

Received  March 2005 Revised  May 2005 Published  March 2006

Applications of three-dimensional Galerkin boundary element methods require the numerical evaluation of many four-dimensional integrals. In this paper we explore the possibility of using extrapolation quadrature. To do so, one needs appropriate error functional expansions. The treatment here is limited to integration over a region $\mathcal T_1 \times \mathcal T_2$, where $\mathcal T_1$ and $\mathcal T_2$ are planar triangular elements in a hanging-chad configuration; that is, they have one vertex in common but are otherwise disjoint. We derive error expansions for product trapezoidal rules valid for integrands having an $|r_{12}|^{-1}$ factor. This factor gives rise to a weak singularity at the common vertex.
Citation: J. N. Lyness. Extrapolation expansions for Hanging-Chad-Type Galerkin integrals with plane triangular elements. Communications on Pure & Applied Analysis, 2006, 5 (2) : 337-347. doi: 10.3934/cpaa.2006.5.337
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