A Note on the Nonconforming Finite Elements for Elliptic Problems

Abstract

In this paper, a class of rectangular finite elements for $2m$-th-oder elliptic boundary value problems in $n$-dimension ($m,n\geq1$) is proposed in a canonical fashion, which includes the ($2m-1$)-th Hermite interpolation element ($n=1$), the $n$-linear finite element ($m=1$) and the Adini element ($m=2$). A nonconforming triangular finite element for the plate bending problem, with convergent order $\mathcal{O}(h^2)$, is also proposed.