  Modeling the unusual mechanical properties of metamaterials is a challenging
topic for the mechanics community and enriched continuum theories are promising
computational tools for such materials. The so-called relaxed micromorphic
model has shown many advantages in this field. In this contribution, we present
the significant aspects related to the relaxed micromorphic model realization
with the finite element method. The variational problem is derived and
different FEM-formulations for the two-dimensional case are presented. These
are a nodal standard formulation $H^1({\cal B}) \times H^1({\cal B})$ and a
nodal-edge formulation $H^1({\cal B}) \times H(\operatorname{curl}, {\cal B})$,
where the latter employs the N\'ed\'elec space. However, the implementation of
higher-order N\'ed\'elec elements is not trivial and requires some
technicalities which are demonstrated. We discuss the convergence behavior of
Lagrange-type and tangential-conforming finite element discretizations.
Moreover, we analyze the characteristic length effect on the different
components of the model and reveal how the size-effect property is captured via
this characteristic length.
