In this paper we develop a leap-frog-type finite element method for modeling the
electromagnetic wave propagation in metamaterials. The metamaterial model equations are represented
by integrodifferential Maxwell’s equations, which are quite challenging to analyze and solve in
that we have to solve a coupled problem with different partial differential equations given in different
material regions. Our method is based on a mixed finite element method using edge elements, which
can easily handle the tangential continuity of the electric field. Stability analysis and optimal error
estimate are carried out for the proposed scheme. The scheme is implemented and confirmed to
obey the proved optimal convergence rate by using a smooth analytical solution. Then the scheme
is extended to model wave propagation in heterogeneous media composed of metamaterials and free
space, and extensive numerical results (using a rectangular edge element, a triangular edge element,
and mixed edge elements) demonstrate the effectiveness of our algorithm for modeling the exotic
backward wave propagation phenomenon in metamaterials. To the best of our knowledge, this is
the first paper with an exhaustive simulation of backward wave propagation in metamaterials using
time-domain finite element methods.