The Babuška-Brezzi condition and the patch test: an example Original Research Article

This paper discusses an example of a mixed finite element method in one dimension which satisfies the engineering patch test, but does not satisfy a uniform inf-sup condition. The inf-sup constant for this method is shown to be of order h2. The reasons for good results from benchmark problems for this method are addressed by characterizing the nature of input data for which the method performs well. Numerical results illustrating the effect of the non-uniform inf-sup condition are presented.