Hello,
Some Finite Element Softwares use the Formulation of an Element and Jump to another one
by Merging Nodes : Quadrilateral to Triangular and Hexahedral to Tetrahedral without modifying
the Shape Functions.
This Method is Mathematically and Numericaly Forbidden because they use the Same Shape Functions
when Merging the Nodes for the Defined First Element (see Element Definition and after Mesh Process).
Gaussian Quadrature Integration has not to be applied to the Second Element with the Functions of the First one.
M.L.