Two families of n-rectangle nonconforming finite elements for sixth-order elliptic equations

03/10/2023

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by   Xianlin Jin, et al.

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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 tri-harmonic 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.