TY - JOUR
T1 - Two Families of $n$-Rectangle Nonconforming Finite Elements for Sixth-Order Elliptic Equations
AU - Jin , Xianlin
AU - Wu , Shuonan
JO - Journal of Computational Mathematics
VL - 1
SP - 121
EP - 142
PY - 2024
DA - 2024/11
SN - 43
DO - http://doi.org/10.4208/jcm.2309-m2023-0052
UR - https://global-sci.org/intro/article_detail/jcm/23532.html
KW - Nonconforming finite element method, $n$-Rectangle element, Sixth-order elliptic equation, Exchange of sub-rectangles.
AB - <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>