The p-version of the boundary element method for weakly singular operators on piecewise plane open surfaces

Alexei Bespalov and Norbert Heuer
Numer. Math. 106 (1), 69-97, 2007.

We study piecewise polynomial approximations in negative order Sobolev norms of singularities which are inherent to Neumann data of elliptic problems of second order in polyhedral domains. The worst case of exterior crack problems in three dimensions is included. As an application, we prove an optimal a priori error estimate for the p-version of the BEM with weakly singular operators on polyhedral surfaces and piecewise plane open screens.