Extrapolation Expansions for Hanging-Chad-Type Galerkin Integrals with Plane Triangular Elements∗
نویسنده
چکیده
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 T1×T2, where T1 and T2 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 |r12|−1 factor. This factor gives rise to a weak singularity at the common vertex.
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