Solution of Maxwell equation in axisymmetric geometry by Fourier series decompostion and by use of H (rot) conforming finite element

Summary. This 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. Received March 15, 1996 / Revised version received November 30, 1998 / Published online December 6, 1999