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
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by S. A. Sauter and C. Lage;

Math. Comp. 70 (2001), 223-250

DOI: https://doi.org/10.1090/S0025-5718-00-01261-8

Published electronically: June 12, 2000

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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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