Some electromagnetic materials present at a particular frequency an effective dielectric permittivity and/or magnetic permeability which are negative. We consider here a scalar model problem for the simulation of wave transmission between a classical material and a ``negative'' one. Introducing additional unknowns, we proposed in \cite{BoCZ07} some new variational formulations of this problem, which are of Fredholm type if the contrast of permittivity is large enough, and therefore suitable for a finite elements discretization. We prove here that, surprisingly, the natural variational formulation of the problem, although not ``coercive plus compact'', is also suitable for a finite elements discretization. Moreover, this numerical approach is less costly than the previous ones.