Solution of Maxwell equation in axisymmetric geometry by Fourier series decomposition and by use of \(H\)(rot) conforming finite element
The Maxwell equations on a bounded 3D domain \(O\) with axial symmetry are considered for the time dependence like \(\exp(i\omega t)\) in a non-resonance case, i.e. \(\omega\) is not an eienvalue of the ``rot rot'' operator on \(O\). Cylindrical coordinates, a Fourier series decomposition, and weighted Sobolev spaces are used to define the weak solution and to propose a numerical approximation. For the latter point, an extension of the Cartesian mixed finite elements of Raviart-Thomas-Nédelec with interpolation error is used.
scientific article; zbMATH DE number 1423202