  In many time-harmonic electromagnetic wave problems, the considered geometry
exhibits an axial symmetry. In this case, by exploiting a Fourier expansion
along the azimuthal direction, fully three-dimensional (3D) calculations can be
carried out on a two-dimensional (2D) angular cross section of the problem,
thus significantly reducing the computational effort. However, the transition
from a full 3D problem to a 2D analysis introduces additional difficulties such
as, among others, a singularity in the variational formulation. In this work,
we compare and discuss different finite element formulations to deal with these
obstacles. Particular attention is paid to spurious modes and to the
convergence behavior when using high-order elements.
