Transformation of hypersingular integrals and black-box cubature

Sauter, S.; Lage, C.

doi:10.1090/S0025-5718-00-01261-8

Transformation of hypersingular integrals and black-box cubature

Authors: S. A. Sauter and C. Lage
Journal: Math. Comp. 70 (2001), 223-250
MSC (2000): Primary 65N38, 65R10, 65R20
DOI: https://doi.org/10.1090/S0025-5718-00-01261-8
Published electronically: June 12, 2000
MathSciNet review: 1803126
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Abstract:

In this paper, we will consider hypersingular integrals as they arise by transforming elliptic boundary value problems into boundary integral equations. First, local representations of these integrals will be derived. These representations contain so-called finite-part integrals. In the second step, these integrals are reformulated as improper integrals. We will show that these integrals can be treated by cubature methods for weakly singular integrals as they exist in the literature.

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