A Finite Element Method to Solve the Maxwell Equations in Three-Dimensional Singular Geometry

We propose to solve a three-dimensional time-dependent Maxwell equations in a singular axisymmetric domain with arbitrary data. Using the axisymmetric assumption, the singular computational domain is reduced to a subset of
$\mathbb{R}^{2}$
, but the electromagnetic field belong to
$\mathbb{R}^{3}$
. By performing a Fourier analysis in one dimension, we get a sequence of singular problems set in a 2D domain, and propose a new finite element approach to solve the problem. Numerical experiments illustrate the method.