(untitled) (Journal of Computational Mathematics, 2020)
Under two hypotheses of nonconforming finite elements of fourth order elliptic problems, we present a side–patchwise projection based error analysis method (SPP–BEAM for short). Such a method is able to avoid both the regularity condition of exact solutions in the classical error analysis method and the complicated bubble function technique in the recent medius error analysis method. In addition, it is universal enough to admit generalizations. Then, we propose a sufficient condition for these hypotheses by imposing a set of in some sense necessary degrees of freedom of the shape function spaces. As an application, we use the theory to design a P_3 second order triangular H^2 non-conforming element by enriching two P_4 bubble functions and, another P_4 second order triangular H^2 nonconforming finite element, and a P_3 second order tetrahedral H^2 non-conforming element by enriching eight P_4 bubble functions, adding some more degrees of freedom.