  In this letter it will be demonstrated explicitly that the finite-element
formulation of quantum electrodynamics is free from fermion doubling. We do
this by (1) examining the lattice fermion propagator and using it to compute
the one-loop vacuum polarization on the lattice, and (2) by an explict
computation of vector and axial-vector current anomalies for an arbitrary
rectangular lattice in the Schwinger model. There it is shown that requiring
that the vector current be conserved necessitates the use of a square lattice,
in which case the axial-vector current is anomalous.
