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

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 / ln k is bounded from below.