@Article{CiCP-34-1332,
author = {Zhang , QianZhang , Min and Zhang , Zhimin},
title = {Nonconforming Finite Elements for the −curl∆curl and Brinkman Problems on Cubical Meshes},
journal = {Communications in Computational Physics},
year = {2023},
volume = {34},
number = {5},
pages = {1332--1360},
abstract = {<p style="text-align: justify;">We propose two families of nonconforming elements on cubical meshes: one
for the −curl∆curl problem and the other for the Brinkman problem. The element
for the −curl∆curl problem is the first nonconforming element on cubical meshes.
The element for the Brinkman problem can yield a uniformly stable finite element
method with respect to the viscosity coefficient $ν.$ The lowest-order elements for the
−curl∆curl and the Brinkman problems have 48 and 30 DOFs on each cube, respectively. The two families of elements are subspaces of $H({\rm curl};Ω)$ and $H({\rm div};Ω),$ and
they, as nonconforming approximation to $H({\rm gradcurl};Ω)$ and $[H^1
(Ω)]^3,$ can form a
discrete Stokes complex together with the serendipity finite element space and the
piecewise polynomial space.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0102},
url = {http://global-sci.org/intro/article_detail/cicp/22216.html}
}