Summary: We consider adaptive mesh refinement for the solution of Maxwell’s equations in the quasi-static or diffusion regime. We propose a new finite volume OcTree discretization for the problem and show how to construct second order stencils on Yee grids, extending the known first order discretization stencils. We then develop an effective preconditioner to the problem. We show that our preconditioner performs well for discontinuous conductivities as well as for a wide range of frequencies.