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 $\pmb{ H}(\mathrm{ curl})$, but not of $\pmb{ H}(\mathrm{ grad}~\mathrm{ curl})$, which are different from the existing nonconforming ones. The well-posedness of the discrete problem is proved and optimal error estimates in discrete $\pmb{ H}(\mathrm{ grad}~\mathrm{ curl})$ norm, $\pmb{ H}(\mathrm{ curl})$ norm and $\pmb{ L}^2$ norm are derived. Numerical experiments are provided to illustrate the good performance of the method and confirm our theoretical predictions.
Categories: math.NA cs.NA