FINITE-ELEMENT DOMAIN APPROXIMATION FOR MAXWELL VARIATIONAL PROBLEMS ON CURVED DOMAINS

We consider the problem of domain approximation in finite element methods for Maxwell equations on general curved domains, i.e., when affine or polynomial meshes fail to exactly cover the domain of interest and an exact parametrization of the surface may not be readily available. In such cases, one is forced to approximate the domain by a sequence of polyhedral domains arising from inexact mesh. We deduce conditions on the quality of these approximations that ensure rates of error convergence between discrete solutions---in the approximate domains---to the continuous one in the original domain. Moreover, we present numerical results validating our claims.