Finite element approximation of Maxwell equations on nonsmooth domains

Time-harmonic Maxwell equations, although being a very simple first-order system, lack some of the standard ellipticity properties that are used in finite element analysis. As a consequence, straightforward finite element approximations on nonsmooth domains may converge to a limit different from the exact solution of the problem. In the talk, I shall discuss the reasons for this, give nuumerical examples, and describe recent progress in overcoming this problem by using a modified variational formulation called "weighted regularization".