High accuracy nonconforming biharmonic element over n‐rectangular meshes

Abstract

This work gives the high accuracy analysis of a rectangular biharmonic element in arbitrarily high-dimensional cases. Given an n-rectangle, we construct the nonconforming finite element and show its explicit standard basis representation. We prove that, if the n-rectangular mesh is uniform, this element can achieve a second order convergence rate in energy norm when applied to biharmonic problems. Numerical examples for n = 3 are also presented.

Two Families of $n$-Rectangle Nonconforming Finite Elements for Sixth-Order Elliptic Equations

“…Furthermore, an extended version of the Morley element to the n-rectangle meshes was also reported in [22]. For the biharmonic equation, a new family of n-rectangle nonconforming finite element by enriching the second-order serendipity element was constructed in [27]. For arbitrary smoothness, a family of minimal n-rectangle macro-elements was established in [16].…”