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

✍ Scribed by Tomás Chacón Rebollo; Antonio Domı́nguez Delgado

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
406 KB
Volume
182
Category
Article
ISSN
0045-7825

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✦ Synopsis

This paper performs a uni®ed 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 coecients, in particular for ¯ows 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 ¯ows. Some numerical test for nonlinear ¯ows show the good performances of this technique.

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