Exponential Convergence of the hp-Version
for the Boundary Element Method on Open Surfaces
Norbert Heuer, Matthias Maischak, Ernst P. Stephan
Numer. Math., 83 (4), 641-666, 1999.
Abstract
We analyze the boundary element Galerkin method for weakly singular
and hypersingular integral equations of the first kind
on open surfaces.
We show that the hp-version of the Galerkin method with
geometrically refined 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 specific singularities
at the corners and the edges of the surface.
We show that these singularities can be efficiently approximated
by piecewise tensor products of splines of different degrees
on geometrically graded meshes.
Numerical experiments supporting these results are presented.