Artículo de publicación ISIWe use Galerkin least-squares terms and biorthogonal wavelet bases to develop a new stabilized dual -mixed finite element method for second order el liptic equations in divergence form with Neumann boundary conditions. The approach introduces the trace of the solution on the boundary as a new unknown that acts also as a Lagrange multiplier. We show that the resulting stabilized dual-mixed variational formulation and the associated discrete scheme defined with Raviart-Thomas spaces are well posed, and derive the usual a-priori error estimates and the corresponding rate of convergence. Furthermore, a reliable and efficient residual based a-posteriori error estimator and a reliable and quasi-efficient one are provided