Resumen
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 [G. Sangalli, Technical report 1221, IAN-CNR, Pavia, Italy, 2001; Numer. Math., to appear], in which we analyze the continuous multidimensional advection-diffusion operator. We obtain these results by means of function space interpolation.