  The time-harmonic Maxwell equations at high wavenumber k in domains with an
analytic boundary and impedance boundary conditions are considered. A
wavenumber-explicit stability and regularity theory is developed that
decomposes the solution into a part with finite Sobolev regularity that is
controlled uniformly in k and an analytic part. Using this regularity,
quasi-optimality of the Galerkin discretization based on Nedelec elements of
order p on a mesh with mesh size h is shown under the k-explicit scale
resolution condition that a) kh/p is sufficient small and b) p/\ln k is bounded
from below.

Numerical Analysis;Numerical Analysis