The diffusion-convection equation in two spatial dimensions is approximated by mixed finite elements using an unsymmetric approach (due to Lesaint/Raviart) for the convection term: For a dissipation parameter \(0\leq \delta \leq 1\), one gets a centered scheme in case \(\delta =0\) and an upwind scheme if \(\delta =1\). (Besides this, there is no indication how to choice that parameter in a practical problem, say in dependence on coefficients and triangulation.) Existence, uniqueness and error estimates are proven in the elliptic and (for the semi-discrete approximation) in the parabolic case, including estimates for diffusion tending to zero.