Scattering of Maxwell's equations with a Leontovich boundary condition in an inhomogeneous medium: A singular perturbation problem

The limiting behavior of the unique solution to the scattering problem for the Maxwell equations with a Leontovich boundary condition in an inhomogene ous medium as the impedance goes to zero is investigated. Making use of a H odge decomposition lemma, it is shown that the Leontovich boundary conditio n leads to a singular perturbation problem for only the scalar unknown in t he Hodge decomposition of the magnetic field. The use of higher-order finit e elements or the refinement of the mesh is then necessary to achieve a suf ficient accuracy of this quantity.