Some $n$-Rectangle Nonconforming Elements for Fourth Order Elliptic Equations

Abstract

In this paper, three $n$-rectangle nonconforming elements are proposed with $n\ge3$. They are the extensions of well-known Morley element, Adini element and Bogner-Fox-Schmit element in two spatial dimensions to any higher dimensions respectively. These elements are all proved to be convergent for a model biharmonic equation in $n$ dimensions.