A Finite Element Approximation of the Stokes Equations

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 finite element approximation. It is shown that the inf-sup stability constant is O(h) in two dimensions and O( ) in three dimensions. The basic tool in the analysis is the method of modified equations which is applied to finite difference representations of the underlying finite 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