Applications of the pseudo residual-free bubbles to the stabilization of convection-diffusion problems

Residual-free bubbles have been recently introduced in order to compute optimal values for the stabilization methods a la Hughes-Franca. However, unless in very special situations (one-dimensional problems, limit cases, etc.) they require the actual solution of PDE problems (the bubble problems) in each element. Thus, they are very difficult to be used in practice. In this paper we present, for the special case of convection-dominated elliptic problems, a cheap way to compute approximately the solution of the bubble problem in each element. This provides, as a consequence, a cheap way to compute good approximations for the optimal values of the stabilization parameters. (C) 1998 Elsevier Science S.A. All rights reserved.