On the convergence of the hp-BEM with quasi-uniform meshes
for the electric field integral equation on polyhedral surfaces
Alexei Bespalov and Norbert Heuer
In this paper the hp-version of the boundary element method is applied to the electric
field integral equation on a piecewise plane (open or closed) Lipschitz surface.
The underlying meshes are supposed to be quasi-uniform.
We use H(div)-conforming discretisations with quadrilateral elements of
Raviart-Thomas type and establish quasi-optimal convergence of hp-approximations.
Main ingredient of our analysis is a new H-1/2(div)-conforming
p-interpolation operator that assumes only
Hr ∩ H-1/2(div)-regularity
(r > 0) and for which we show quasi-stability with respect to polynomial degrees.