A critical study of hypersingular and strongly singular boundary integral representations of potential gradient
This paper deals with recovery of all first derivatives (not only the normal derivative!) of functions which are given in form of a direct boundary integral representation consisting of simple and double layer potentials for the Laplacian in two-dimensional domains with piecewise smooth Lipschitz boundary. Especially, the evaluation near and on the boundary is of interest. Four different methods for calculating the derivatives are described and their accuracy and convergence behaviour is investigated. Several numerical tests for comparing the different methods are included.
scientific article; zbMATH DE number 1491159