An anisotropic, superconvergent nonconforming plate finite element

The classical finite element convergence analysis relies on the following regularity condition: there exists a constant c independent of the element K and the mesh such that hK/ρK⩽c, where hK and ρK are diameters of K and the biggest ball contained in K, respectively. In this paper, we construct a new, nonconforming rectangular plate element by the double set parameter method. We prove the convergence of this element without the above regularity condition. The key in our proof is to obtain the O(h2) consistency error. We also prove the superconvergence of this element for narrow rectangular meshes. Results of our numerical tests agree well with our analysis.