The influence of the choice of connectors in the finite element method

The patch test is interpreted from a variational point of view. This leads to conclude that non conforming (or non stress diffusive) displacement (stress) models can be considered as special hybrid models. A simple choice of mixed connectors is proposed that satisfy a priori the patch test for any assumed displacement or stress field. Finally some numerical examples are given of finite elements that do not pass the patch test but still converge.