On the stability of finite-element discretizations of convection-diffusion-reaction equations

A priori error estimates for the local projection (LP) stabilization applied to convection-diffusion-reaction equations are generally based on the coercivity of the underlying bilinear form with respect to the LP norm. We show that the bilinear form of the LP stabilization satisfies an inf-sup condition in a stronger norm that is equivalent to that of the streamline upwind/Petrov-Galerkin method. As a consequence, we get some insight into the stabilization mechanism of Galerkin discretizations of higher order.