The hp-version of the boundary element method with quasi-uniform meshes
for weakly singular operators on surfaces
Alexei Bespalov and Norbert Heuer
IMA J. Numer. Anal. 30 (2), 377-400, 2010.
We prove an a priori error estimate for the hp-version of the boundary
element method with weakly singular operators in three dimensions.
The underlying meshes are quasi-uniform. Our model problem is that of the
Laplacian exterior to an open surface where the solution has strong
singularities which are not L2-regular.
Our results confirm previously conjectured convergence rates in h
(the mesh size) and p (the polynomial degrees) and these rates are
given explicitly in terms of the exponents of the singular functions.
In particular, for sufficiently smooth given data we prove a convergence in
the energy norm like O(h½p-1).