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.

翻译：本文研究具有解析边界和阻抗边界条件的高波数k区域中的时谐麦克斯韦方程。建立了波数显式的稳定性与正则性理论，将解分解为具有有限Sobolev正则性（在k上一致可控）的部分和分析部分。利用该正则性，证明了在k显式尺度分辨率条件下，基于网格尺寸h和阶数p的Nédélec元Galerkin离散化的拟最优性：（a）kh/p足够小，（b）p/ln k有下界。