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

Abstract : 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.
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https://hal-cea.archives-ouvertes.fr/cea-03578610
Contributor : Patrick Lacoste Connect in order to contact the contributor
Submitted on : Thursday, February 17, 2022 - 1:43:59 PM
Last modification on : Saturday, February 19, 2022 - 3:07:09 AM
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Patrick Lacoste. Solution of Maxwell equation in axisymmetric geometry by Fourier series decompostion and by use of H(rot) conforming finite element. Numerische Mathematik, Springer Verlag, 2000, Numer. Math. 84, 577–609 (2000), pp.577-609. ⟨10.1007/s002119900112⟩. ⟨cea-03578610⟩

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