Weighted regularization of Maxwell equations in polyhedral domains - A rehabilitation of Nodal finite elements

We present a new method of regularizing time harmonic Maxwell equations by a grad-div term adapted to the geometry of the domain. This method applies to polygonal domains in two dimensions as well as to polyhedral domains in three dimensions. In the presence of reentrant corners or edges, the usual regularization is known to produce wrong solutions due the non-density of smooth fields in the variational space. We get rid of this undesirable effect by the introduction of special weights inside the divergence integral. Standard finite elements can then be used for the approximation of the solution. This method proves to be numerically efficient.