Simulation of electromagnetic wave propagation in metamaterials
leads to more complicated time domain Maxwell's equations than the standard Maxwell's equations in free space.
In this paper, we develop and analyze a non-dissipative
discontinuous Galerkin (DG) method for solving the Maxwell's equations
in Drude metamaterials.
Previous discontinuous Galerkin methods in the literature
for electromagnetic wave propagation in metamaterials were either
non-dissipative but sub-optimal, or dissipative and optimal. Our
method uses a different and simple choice of numerical fluxes,
achieving provable non-dissipative stability and optimal error
estimates simultaneously.
We prove the stability and optimal error estimates for both semi- and
fully discrete DG schemes, with the leap-frog time discretization
for the fully discrete case. Numerical results are given to
demonstrate that the DG method can solve metamaterial Maxwell's
equations effectively.