  We consider H(curl)-elliptic variational problems on bounded Lipschitz
polyhedra and their finite element Galerkin discretization by means of lowest
order edge elements. We assume that the underlying tetrahedral mesh has been
created by successive local mesh refinement, either by local uniform refinement
with hanging nodes or bisection refinement. In this setting we develop a
convergence theory for the the so-called local multigrid correction scheme with
hybrid smoothing. We establish that its convergence rate is uniform with
respect to the number of refinement steps. The proof relies on corresponding
results for local multigrid in a H1-context along with local discrete
Helmholtz-type decompositions of the edge element space.
