Further considerations on residual-free bubbles for advective-diffusive equations

We further consider the Galerkin method for advective-diffusive equations in two dimensions. The finite dimensional space employed is of piecewise polynomials enriched with residual-free bubbles (RFB). We show that, in general, this method does not coincide with the SUPG method, unless the piecewise polynomials are spanned by linear functions. Furthermore, a simple stability analysis argument displays the effect of the RFB on the reduced space of piecewise polynomials, which, in some situations, is not equivalent to streamline diffusion for bilinears