Finite element analysis of a time harmonic Maxwell problem with an impedance boundary condition

We consider an electromagnetic scattering problem produced by a perfect conductor. We pose the problem in a bounded region surrounding the obstacle and impose on the exterior boundary of the computational domain an impedance boundary condition inspired by the asymptotic behaviour of the scattered field at infinity. The operator associated with our problem belongs to a class of operators for which a suitable decomposition of the energy space plays an essential role in the analysis. This decomposition is performed here through a regularizing projector that takes into account the boundary conditions. The discrete version of this projector is the key tool to prove that a Galerkin scheme based on Nedelec's edge elements is well posed and convergent under general topological assumptions on the scatterer and without assuming special requirements on the triangulations.