as follows. In Section \[sec:preliminaries\], we briefly recall the Maxwell equations and we introduce the notation for the treatment of problems in axisymmetric domains. Section \[sec:discretization\] is devoted to the presentation of the strategy used to extend a general discretization in Cartesian coordinate to the cylindrical setting. Moreover, appropriate error estimates are introduced. In Section \[sec:iga\], we briefly introduce the discrete spaces used for , together with error estimates, that will be used to build the discretization presented in Section \[sec:discretization\]. In Section \[sec:tests\], we apply the method presented in this work to relevant problems often arising in electromagnetism. Finally, in Section \[sec:conclu\], we draw conclusions and discuss possible future developments of the proposed approach.

Preliminaries {#sec:preliminaries}
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Consider the time-harmonic Maxwell equations [@jackson:2007; @monk:2003] $$\label{eq:max_eq}
\begin{aligned}
\curlt \Ev & = i\omega\,{\Bv}~,\\
\divergt \Dv & =\chargeden~, \\
\curlt \Hv & = \jv -i\omega\,{\Dv}~,\\
\divergt \Bv & = 0~, %\label{eq:iwmax_diff_noBsource}
\end{aligned}$$ together with the magnetic vector potential $\magvp$, for which $$\Bv = \curlt \magvp$$ holds, and a set of linear constitutive relations that links the fluxes $\Dv$ and $\Bv$ to the field strengths $\Ev$ and $\Hv$: $$\Dv = \pmitt \Ev~, \qquad \Bv = \pmeab \Hv~,$$ where $\pmitt$ and $\pmeab$ are the 