Numerical analysis of a model for an axisymmetric guide for electromagnetic waves Part I: the continuous problem and its Fourier expansion
✍ Scribed by Faker Ben Belgacem; Christine Bernardi; Francesca Rapetti
- Publisher
- John Wiley and Sons
- Year
- 2005
- Tongue
- English
- Weight
- 205 KB
- Volume
- 28
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.649
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✦ Synopsis
Abstract
SUMMARY
As a first model for an electromagnetic wave guide, we consider Maxwell's system in a three‐ dimensional axisymmetric domain provided with appropriate boundary conditions on different parts of the boundary. We check the well‐posedness of the corresponding variational problem. We write the Fourier expansion of the solution as a function of the angular variable and derive the well‐posedness of the two‐dimensional problems satisfied by each Fourier coefficient. The first step for approximating the three‐dimensional solution relies on Fourier truncation, and we prove optimal estimates for the error issued from this truncation. Copyright © 2005 John Wiley & Sons, Ltd.