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

Patrick Lacoste (1)

1 CESTA - Centre d'études scientifiques et techniques d'Aquitaine

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.

Domaines: Mathématiques [math]

Patrick Lacoste. Solution of Maxwell equation in axisymmetric geometry by Fourier series decompostion and by use of H(rot) conforming finite element. Numerische Mathematik, 2000, Numer. Math. 84, 577–609 (2000), 84, pp.577-609. ⟨10.1007/s002119900112⟩. ⟨cea-03578610⟩