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

Jens Markus Melenk, Stefan Sauter

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 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) $p/\log k$ is bounded from below.

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