A unified analysis of mixed and stabilized finite element solutions of Navier-Stokes equations

This paper performs a unified numerical analysis of Mixed and Stabilized Finite Element numerical solutions of 2D and 3D Steady Navier-Stokes Equations. We introduce a general internal discretization of Navier-Stokes equations of which both Mixed and Stabilized Methods are particular cases. We prove convergence of Stabilized Methods with non linear stabilization coefficients, in particular for flows with convection dominance. We also analyze the approximation of branches of regular solutions, in the case of convection dominance. We introduce a stabilized post-processing of Galerkin Finite Element (FE) solution of convection-dominated flows. Some numerical test for nonlinear flows show the good performances of this technique. (C) 2000 Elsevier Science S.A. All rights reserved.