@Article{CiCP-33-1069, author = {Zhang , Baiju and Zhang , Zhimin}, title = {A New Family of Nonconforming Elements with $H$(curl)-Continuity for the 3D Quad-Curl Problem}, journal = {Communications in Computational Physics}, year = {2023}, volume = {33}, number = {4}, pages = {1069--1089}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2022-0216}, url = {http://global-sci.org/intro/article_detail/cicp/21669.html} }