  In nodal based finite element method (FEM), degrees of freedom are associated
with the nodes of the element whereas, for edge FEM, degrees of freedom are
assigned to the edges of the element. Edge element is constructed based on
Whitney spaces. Nodal elements impose both tangential and normal continuity of
vector or scalar fields across interface boundaries. But in edge elements only
tangential continuity is imposed across interface boundaries, which is
consistent with electromagnetic field problems. Therefore, the required
continuities in the electromagnetic analysis are directly obtained with edge
elements, whereas in nodal elements they are attained through potential
formulations. Hence, while using edge elements, field variables are directly
calculated, but with nodal elements, post-processing is required to obtain the
field variables from the potentials. Here, we present the finite element
formulations with the edge element as well as with nodal elements. Thereafter,
we have demonstrated the relative performances of different nodal and edge
elements through a series of examples. All possible complexities like curved
boundaries, non-convex domains, sharp corners, non-homogeneous domains have
been addressed in those examples. The robustness of edge elements in predicting
the singular eigen values for the domains with sharp edges and corners is
evident in the analysis. A better coarse mesh accuracy has been observed for
all the edge elements as compared to the respective nodal elements. Edge
elements are also not susceptible to mesh distortion.
