We consider time harmonic Maxwell equations in a bounded Lipschitz polyhedron with perfectly conducting boundary. Among the available Galerkin methods, we choose the approximation obtained by edge elements. Due to the presence of singularities, the convergence of the scheme for uniform meshes is very poor. Given a $k\in \mathbb{N}$, we design a suitable refining technique ensuring the speed of convergence to be of order $ N^{k/3}$, $N$ being the total number of degrees of freedom.