A Finite Element Approximation of the Stokes Equations

Samy Alami, Abdeslam Elakkad, Jawad El-Mekaoui, Ahmed Elkhalfi, Mohammed El Hammoumi

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DOI: 10.4236/wjm.2011.16038                

Abstract

In this work, a numerical solution of the incompressible Stokes equations is proposed. The method suggested is based on an algorithm of discretization by the unstable of Q₁ – P₀ velocity/pressure ?nite element approximation. It is shown that the inf-sup stability constant is O(h) in two dimensions and O( h₂) in three dimensions. The basic tool in the analysis is the method of modi?ed equations which is applied to ?nite difference representations of the underlying ?nite element equations. In order to evaluate the performance of the method, the numerical results are compared with some previously published works or with others coming from commercial code like Adina system.

Keywords

Stokes Equations, Finite Element Method, Iterative Solvers, Adina System

Conflicts of Interest

The authors declare no conflicts of interest.

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