Optimal superconvergence analysis for the Crouzeix-Raviart and the Morley elements

In this paper, an improved superconvergence analysis is presented for both the Crouzeix-Raviart element and Morley element. The main idea of to employ a discrete Helmholtz decomposition difference between canonical interpolation finite solution first-order mixed Raviart–Thomas Hellan–Herrmann–Johnson element, respectively. This in particular allows proving full one-order result these two elements. Finally, follows from their special relations with Those results are also extended mildly structured meshes.