Auxiliary space preconditioners for a DG discretization of H(curl; Omega)-elliptic problem on hexahedral meshes

We present a family of preconditioners based on the auxiliary space method for a discontinuous Galerkin discretization on cubical meshes of H(curl;?)-elliptic problems with possibly discontinuous coefficients. We address the influence of possible discontinuities in the coefficients on the asymptotic performance of the proposed solvers and present numerical results in two dimensions.