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On the solution of Maxwell's equations in polygonal domains

✍ Scribed by Boniface Nkemzi

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
287 KB
Volume
29
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

This paper is concerned with the structure of the singular and regular parts of the solution of time‐harmonic Maxwell's equations in polygonal plane domains and their effective numerical treatment. The asymptotic behaviour of the solution near corner points of the domain is studied by means of discrete Fourier transformation and it is proved that the solution of the boundary value problem does not belong locally to H^2^ when the boundary of the domain has non‐acute angles. A splitting of the solution into a regular part belonging to the space H^2^, and an explicitly described singular part is presented. For the numerical treatment of the boundary value problem, we propose a finite element discretization which combines local mesh grading and the singular field methods and derive a priori error estimates that show optimal convergence as known for the classical finite element method for problems with regular solutions. Copyright © 2006 John Wiley & Sons, Ltd.

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