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The consistency of the approximation of a double-layer potential when using a boundary-element method and approximating the curved boundary by a polygonal curve in two-dimensional problems or by a polyhedral surface in three-dimensional ones is investigated. The results are applied to the numerical analysis of the approximation of a model problem: the diffraction of a time-harmonic acoustic wave by a penetrable object.

mathematics of computation

Consistency estimates for a double-layer potential and application to the numerical analysis of the boundary-element approximation of acoustic scattering by a penetrable object