Wavenumber-explicit hp-FEM analysis for Maxwell’s equations with transparent boundary conditions

Abstract

The time-harmonic Maxwell equations at high wavenumber k are discretized by edge elements of degree p on a mesh of width h. For the case of a ball as the computational domain and exact, transparent boundary conditions, we show quasi-optimality of the Galerkin method under the k-explicit scale resolution condition that (a) kh/p is sufficient small and (b) p/lnk is bounded from below.