A New Family of Nonconforming Elements with H(curl)-Continuity for the 3D Quad-Curl Problem

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 H(curl), but not of 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 H(grad curl) norm, H(curl) norm and L2 norm are derived. Numerical experiments are provided to illustrate the good performance of the method and confirm our theoretical predictions.