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

We investigate the finite element methods for solving time-dependent Maxwel l equations with discontinuous coefficients in general three-dimensional Li pschitz polyhedral domains. Both matching and nonmatching finite element me shes on the interfaces are considered, and optimal error estimates for both cases are obtained. The analysis of the latter case is based on an abstrac t 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 d eriving discrete inf-sup conditions.