Lessons for incompressible and near-incompressible elasticity drawn from the driven cavity flow problem

A range of low order elements are applied to the driven cavity flow problem. These include pure displacement elements, mixed pressure-displacement and enhanced strain elements, with the latter sometimes being combined with mixed pressure-displacement formulations. The problem is analysed in two ways; first using Chapelle and Bathe’s numerical implementation of the ‘inf-sup test’ and secondly via a direct numerical analysis with increasing bulk modulus. As a result of these two sets of tests, insights are gained into the potential performance of these elements for the general incompressible (or nearly incompressible) elasticity and elasto-plasticity problems.