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- W1971691608 abstract "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. Comme modèle de base d'un guide d'ondes électromagnétiques, nous considérons les équations de Maxwell dans un domaine tri-dimensionnel axisymétrique, munies de conditions aux limites adéquates sur différentes parties de la frontière. Nous prouvons que le problème variationnel correspondant est bien posé. Nous écrivons le développement en série de Fourier de la solution par rapport à la variable angulaire et constatons que les problèmes bi-dimensionnels vérifiés par chaque coefficient de Fourier sont également bien posés. La première idée pour construire une approximation de la solution tri-dimensionnelle consiste en une troncature en Fourier, et nous établissons des majorations optimales de l'erreur dues a cette troncature." @default.
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- W1971691608 date "2005-01-01" @default.
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- W1971691608 title "Numerical analysis of a model for an axisymmetric guide for electromagnetic waves Part I: the continuous problem and its Fourier expansion" @default.
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- W1971691608 doi "https://doi.org/10.1002/mma.649" @default.
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