Year: 2025
Author: Xianlin Jin, Shuonan Wu
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 1 : pp. 121–142
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2309-m2023-0052
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 1 : pp. 121–142
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Nonconforming finite element method $n$-Rectangle element Sixth-order elliptic equation Exchange of sub-rectangles.