I mean, when studying plate bending elements I arrived to a non-conforming element which according to the literature the displacement along a common side between two elements may not be the same. So, my point is: what's the explanation for these elements converge if one of the FEM criterias of convergence is the compatibility of displacement between these elements?
FEA solves for displacement compatibility at the nodes. Non-conforming plate elements will have compatible displacements at the nodes, but the displacements in between may be different.