Recovering SUPG using Petrov-Galerkin formulations enriched with adjoint residual-free bubbles

We consider conforming Petrov-Galerkin formulations for the advective and a dvective-diffusive equations. For the linear hyperbolic equation, the conti nuous formulation is set up using different spaces and the discretization f ollows with different "bubble" enrichments for the test and trial spaces. B oundary conditions for residual-free bubbles are modified to accommodate wi th the first-order equation case and regular bubbles are used to enrich the other space. Using piecewise linears with these enrichments, the final for mulations are shown to be equivalent to the SUPG method, provided the data are assumed to be piecewise constant. Generalization to include diffusion i s also presented. (C) 2000 Elsevier Science S.A. All rights reserved.