In this paper, we describe a new continuous approximation of Maxwell’s equations well-suited to mass-lumping and which ensures low storage. Then, we introduce a dissipative jump derived from Discontinuous Galerkin Methods (DGM) to get rid of spurious waves for both edge and continuous elements. This new approach leads to efficient spectral elements for Maxwell’s equations which are cheaper than DGM. On the other hand, this approach provides a good approximation of singularities generated by reentrant corners.