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

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 controlle...

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Bibliographic Details
Published in:arXiv.org 2023-08
Main Authors: Melenk, Jens M, Sauter, Stefan A
Format: Article
Language:English
Subjects:
Boundary conditions
Finite element method
Impedance
Mathematical analysis
Maxwell's equations
Regularity
Stability analysis
Wavelengths
Online Access:Get full text
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Summary: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.
ISSN:2331-8422