  The inf-sup condition, also called the Ladyzhenskaya--Babu\v ska--Brezzi
(LBB) condition, ensures the existence, uniqueness and well-posedness of a
saddle point problem, relative to a partial differential equation.
Discretization by the finite element method gives the discrete problem which
must satisfy the discrete inf-sup condition. But, depending on the choice of
finite elements, the discrete condition may fail. This paper attempts to
explain why it fails from an engineer's perspective, and reviews current
methods to work around this failure. The last part recalls the mathematical
bases.
