  In this paper we develop a finite element method for acoustic wave
propagation in Drude-type metamaterials. The governing equation is written as a
symmetrizable hyperbolic system with auxiliary variables. The standard mixed
finite elements and discontinuous finite elements are used for spatial
discretization, and the Crank-Nicolson scheme is used for time discretization.
The a priori error analysis of fully discrete scheme is carried out in details.
Numerical experiments illustrating the theoretical results and metamaterial
wave propagation, are included.
