Quasi-optimality of the SUPG method for the one-dimensional advection-diffusion problem

In this paper we propose quasi-optimal error estimates, in various norms, for the Streamline-Upwind Petrov-Galerkin (SUPG) method applied to the linear one-dimensional advection-diffusion problem. We follow the classical argument due to Babuska and Brezzi, therefore the goal of this work is the proof of the inf-sup and of the continuity conditions for the bilinear stabilized variational form, with respect to suitable norms. These norms are suggested by our previous work [9], in which we analyze the continuous multidimensional advection-diffusion operator. We obtain these results by means of functional spaces interpolation.