Applications of the pseudo residual-free bubbles to the stabilization of the convectiondiffusionreaction problems in 2D
A stabilized finite element method is studied herein for two-dimensional convectiondiffusionreaction problems. The method is based on the residual-free bubbles (RFB) method. However we replace the RFB functions by their cheap, yet efficient approximations computed on a specially chosen subgrid, which retain the same qualitative behavior. Since the correct spot of subgrid points plays a crucial role in the approximation, it is important to determine their optimal locations, which we do it through a minimization process with respect to the L1 L 1 -norm. The resulting numerical method has similar stability features with the well-known stabilized methods in the literature for the whole range of problem parameters and this fact is also confirmed by numerical experiments.
pseudo residual-free bubbles stabilized finite element methods augmented space