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 -

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.