APPLICATIONS OF THE PSEUDO RESIDUAL-FREE BUBBLES TO THE STABILIZATIONOF CONVECTION-DIFFUSION PROBLEMS

Residual-free bubbles have been recently introduced in order to comput e optimal values for the stabilization methods a la Hughes-Franca. How ever, unless in very special situations (one-dimensional problems, lim it 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 co nvection-dominated elliptic problems, a cheap way to compute approxima tely 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 Sci ence S.A. All rights reserved.