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.
Highlights
It is universally recognized that discretization schemes for Stokes and Navier-Stokes equations are subject to an inf-sup or div-stability condition [1]
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
Summary
It is universally recognized that discretization schemes for Stokes and Navier-Stokes equations are subject to an inf-sup or div-stability condition [1]. The stability requirement is manifested in practical computations by the predominance of staggered grid finite volume discretizations, and the existence of unnatural velocity-pressure finite element combinations. These typically involve velocity bubble functions, or else have a macro-element definition of the velocity field. A number of stabilization methods for inf-sup unstable approximations have been developed during the last three decades. These methods can be classified into two kinds. In this paper the low order conforming finite element methods like Q1 P0 (trilinear/bilinear velocity with constant pressure) for incompressible flow problems are characterised.
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