Wavenumber-Explicit hp-FEM Analysis for Maxwell’s Equations with Impedance Boundary Conditions

Abstract

The time-harmonic Maxwell equations at high wavenumberkin 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 inkand an analytic part. Using this regularity, quasi-optimality of the Galerkin discretization based on Nédélec elements of orderpon a mesh with mesh sizehis shown under thek-explicit scale resolution condition that (a)kh/pis sufficient small and (b)$p/\ln k$is bounded from below.