(untitled) (Journal of Computational Mathematics, 2024)
In this paper, we propose two families of nonconforming finite elements on n-rectangle meshes of any dimension to solve the sixth-order elliptic equations. The unisolvent property and the approximation ability of the new finite element spaces are established. A new mechanism, called the exchange of sub-rectangles, for investigating the weak continuities of the proposed elements is discovered. With the help of some conforming relatives for the H^3 problems, we establish the quasi-optimal error estimate for the triharmonic equation in the broken H^3 norm of any dimension. The theoretical results are validated further by the numerical tests in both 2D and 3D situations.