Exponential convergence of the hp-version for the boundary element method on open surfaces

We analyze the boundary element Galerkin method for weakly singular and hypersingular integral equations of the rst kind on open surfaces. We show that the hp-version of the Galerkin method with geometrically reened meshes converges exponentially fast for both integral equations. The proof of this fast convergence is based on the special structure of the solutions of the integral equations which possess speciic singularities at the corners and the edges of the surface. We show that these singularities can be eeciently approximated by piecewise tensor products of splines of diierent degrees on geometrically graded meshes. Numerical experiments supporting these results are presented.