A nodal-based finite element approximation of the Maxwell problem suitable for singular solutions

Abstract

A new mixed finite element approximation of Maxwell's problem is proposed, its main features being that it is based on a novel augmented formulation of the continuous problem and the introduction of a mesh dependent stabilizing term, which yields a very weak control on the divergence of the unknown. The method is shown to be stable and convergent in the natural $H(curl0;\Omega )$ norm for this unknown. In particular, convergence also applies to singular solutions, for which classical nodal-based interpolations are known to suffer from spurious convergence upon mesh refinement.