TY - JOUR
T1 - A New Family of Nonconforming Elements with $H$(curl)-Continuity for the 3D Quad-Curl Problem
AU - Zhang , Baiju
AU - Zhang , Zhimin
JO - Communications in Computational Physics
VL - 4
SP - 1069
EP - 1089
PY - 2023
DA - 2023/05
SN - 33
DO - http://doi.org/10.4208/cicp.OA-2022-0216
UR - https://global-sci.org/intro/article_detail/cicp/21669.html
KW - Quad-curl problem, nonconforming finite element method.
AB - <p style="text-align: justify;">We propose and analyze a new family of nonconforming finite elements
for the three-dimensional quad-curl problem. The proposed finite element spaces are
subspaces of $\boldsymbol{H}$(curl), but not of $\boldsymbol{H}$(grad curl), which are different from the existing
nonconforming ones [10,12,13]. The well-posedness of the discrete problem is proved
and optimal error estimates in discrete $\boldsymbol{H}$(grad curl) norm, $\boldsymbol{H}$(curl) norm and $L^2$ norm
are derived. Numerical experiments are provided to illustrate the good performance
of the method and confirm our theoretical predictions.</p>