On the convergence of the hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces

Abstract

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 $\bH(\div)$-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 $\tilde\bH^{-1/2}(\div)$-conforming p-interpolation operator that assumes only $\bH^r\cap\tilde\bH^{-1/2}(\div)$-regularity ($r>0$) and for which we show quasi-stability with respect to polynomial degrees.