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We prove an optimal a priori error estimate for the hp-version of the boundary element method with hypersingular operators on piecewise plane open or closed surfaces. The un- derlying meshes are supposed to be quasi-uniform. The solutions of problems on polyhedral or piecewise plane open surfaces exhibit typical singularities which limit the convergence rate of the boundary element method. On closed surfaces, and for sucien tly smooth given data, the solution is H 1-regular whereas, on open surfaces, edge singularities are strong enough to prevent the solution from being in H 1. In this paper we cover both cases and, in particular, prove an optimal a priori error esti- mate for the h-version with quasi-uniform meshes. For open surfaces we prove a convergence like O(h1=2p 1), h being the mesh size and p denoting the polynomial degree.

Thehp-version of the boundary element method with quasi-uniform meshes in three dimensions