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

Wavenumber-explicit hp-FEM analysis for Maxwell's equations with impedance boundary conditions