https://hal-cea.archives-ouvertes.fr/cea-03578610Lacoste, PatrickPatrickLacosteCESTA - Centre d'études scientifiques et techniques d'Aquitaine - DAM - Direction des Applications Militaires - CEA - Commissariat à l'énergie atomique et aux énergies alternativesSolution of Maxwell equation in axisymmetric geometry by Fourier series decompostion and by use of H(rot) conforming finite elementHAL CCSD2000[MATH] Mathematics [math]Lacoste, Patrick2022-02-17 13:43:592022-02-19 03:07:092022-02-18 09:37:54enJournal articleshttps://hal-cea.archives-ouvertes.fr/cea-03578610/document10.1007/s002119900112application/pdf1This study deals with the mathematical and numerical solution of time-harmonic Maxwell equation in axisymmetric geometry. Using Fourier decomposition, we define weighted Sobolev spaces of solution and we prove expected regularity results. A practical contribution of this paper is the construction of a class of finite element conforming with the H(rot) space equipped with the weighted measure rdrdz. It appears as an extension of the well-known cartesian mixed finite element of Raviart-Thomas-Nédélec [11]-[15]. These elements are built from classical lagrangian and mixed finite element, therefore no special approximations functions are needed. Finally, following works of Mercier and Raugel [10], we perform an interpolation error estimate for the simplest proposed element.