@Article{JCM-43-121,
author = {Jin , Xianlin and Wu , Shuonan},
title = {Two Families of $n$-Rectangle Nonconforming Finite Elements for Sixth-Order Elliptic Equations},
journal = {Journal of Computational Mathematics},
year = {2024},
volume = {43},
number = {1},
pages = {121--142},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2309-m2023-0052},
url = {http://global-sci.org/intro/article_detail/jcm/23532.html}
}