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

Inf-sup condition and locking: Understanding and circumventing. Stokes,  Laplacian, bi-Laplacian, Kirchhoff--Love and Mindlin--Reissner locking type,  boundary conditions