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Abstract

In this paper, we analyze a class of stabilized finite element formulations used in computation of (i) second order elliptic boundary value problems (diffusion-convection-reaction model) and (ii) the Navier-Stokes problem (incompressible flow model). These stabilization techniques prevent numerical instabilities that might be generated by dominant convection/reaction terms in (i), (ii) or by inappropriate combinations of velocity/pressure interpolation functions in (ii). Stability and convergence results on non-uniform meshes are given in the whole range from diffusion to convection/reaction dominated situations. In particular, we recover results for the streamline upwind and Galerkin/least-squares methods. Numerical results are presented for low order interpolation functions.