A New Family of Nonconforming Elements with $H$(curl)-Continuity for the 3D Quad-Curl Problem (Communications in Computational Physics, 2023)
We propose and analyze a new family of nonconforming finite elementsfor the three-dimensional quad-curl problem. The proposed finite element spaces aresubspaces of $\boldsymbol{H}$(curl), but not of $\boldsymbol{H}$(grad curl), which are different from the existingnonconforming ones [10,12,13]. The well-posedness of the discrete problem is provedand optimal error estimates in discrete $\boldsymbol{H}$(grad curl) norm, $\boldsymbol{H}$(curl) norm and $L^2$ normare derived. Numerical experiments are provided to illustrate the good performanceof the method and confirm our theoretical predictions.