The inf–sup condition and its evaluation for mixed finite element methods

The objective of this paper is to review the general inf–sup condition for mixed finite element methods and summarize numerical procedures (inf–sup tests) for the evaluation of the inf–sup expressions specific to various problem areas. The inf–sup testing of a given mixed finite element discretization is most important in order to assess its reliability and solution effectiveness. The problem areas considered are (almost) incompressible analysis of solids and fluids, acoustic fluids, the analysis of plates and shells, and the solution of convection-dominated flows.