  Finite element representations of Maxwell's equations pose unusual challenges
inherent to the variational representation of the `curl-curl' equation for the
fields. We present a variational formulation based on classical field theory.
Borrowing from QED, we modify the Lagrangian by adding an implicit gauge-fixing
term. Our formulation, in the language of differential geometry, shows that
conventional edge elements should be replaced by the simpler nodal elements for
time-harmonic problems. We demonstrate how this formulation, adhering to the
deeper underlying symmetries of the four-dimensional covariant field
description, provides a highly general, robust numerical framework.
