Natural Boundary Element Methods for the Electric Field Integral Equation on Polyhedra

We consider the electric field integral equation on the surface of polyhedral domains and its Galerkin discretization by means of divergence-conforming boundary elements. With respect to a Hodge decomposition, the continuous variational problem is shown to be coercive. However, this does not immediately carry over to the discrete setting, as discrete Hodge decompositions fail to possess essential regularity properties. Introducing an intermediate semidiscrete Hodge decomposition, we can bridge the gap and come up with asymptotically optimal a priori error estimates. Until now, those had been elusive, in particular for nonsmooth boundaries.