Finite element methods with matching and nonmatching meshes for Maxwell equations with discontinuous coefficients

We investigate the finite element methods for solving time-dependent Maxwell equations with discontinuous coefficients in general three-dimensional Lipschitz polyhedral domains. Both matching and nonmatching finite element meshes on the interfaces are considered, and optimal error estimates for both cases are obtained. The analysis of the latter case is based on an abstract framework for nested saddle point problems, along with a characterization of the trace space for H(curl; D), a new extension theorem for H(curl; D) functions in any Lipschitz domain D, and a novel compactness argument for deriving discrete inf-sup conditions.