  In this paper, we consider the frequency-domain Maxwell's equations coupled
to a nonlocal Drude model which describes the nonlocal optical response in
metallic nanostructures. We prove the existence and uniqueness of weak
solutions to the coupled equations. A Galerkin finite element method based on
the Raviart--Thomas and N\'{e}d\'{e}lec elements is proposed to solve the
equations and the associated error estimates are given. This is the first work
on the mathematical and numerical analysis of this model. Numerical examples
are presented to verify our theoretical analysis.
