2022/01/07 by Jens Markus Melenk, Melenk, Jens M., Stefan Sauter +1 · 1 citation
Engineering · #Electromagnetic Simulation and Numerical Methods #Numerical methods in engineering #Advanced Numerical Methods in Computational Mathematics
paper · doi:10.48550/arxiv.2201.02602
The time-harmonic Maxwell equations at high wavenumber k in 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 in k and an analytic part. Using this regularity, quasi-optimality of the Galerkin discretization based on Nedelec elements of order p on a mesh with mesh size h is shown under the k-explicit scale resolution condition that a) kh/p is sufficient small and b) p/ln k is bounded from below.