In this article, we consider the time-dependent Maxwell’s equations modeling wave propagation in metamaterials.
One-order higher global superclose results in the L2 norm are proved for several semidiscrete
and fully discrete schemes developed for solving this model using nonuniform cubic and rectangular edge
elements. Furthermore, L
∞ superconvergence at element centers is proved for the lowest order rectangular
edge element. To our best knowledge, such pointwise superconvergence result and its proof are original, and
we are unaware of any other publications on this issue.