Author:
Melenk J. M.,Sauter S. A.
Abstract
AbstractThe time-harmonic Maxwell equations at high wavenumberkin 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 inkand an analytic part. Using this regularity, quasi-optimality of the Galerkin discretization based on Nédélec elements of orderpon a mesh with mesh sizehis shown under thek-explicit scale resolution condition that (a)kh/pis sufficient small and (b)$$p/\ln k$$p/lnkis bounded from below.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Theory and Mathematics,Computational Mathematics,Analysis
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