Abstract
In this paper, we develop both semi-discrete and fully-discrete mixed finite element methods for modeling wave propagation in three-dimensional double negative metamaterials. Here the model is formed as a time-dependent linear system involving four dependent vector variables: the electric and magnetic fields, and the induced electric and magnetic currents. Optimal error estimates for all four variables are proved for Nedelec tetrahedral elements. To our best knowledge, this is the first error analysis obtained for Maxwell's equations when metamaterials are involved.
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