Distributional Finite Element curl div Complexes and Application to Quad Curl Problems

The paper addresses the challenge of constructing conforming finite element spaces for the curl div operator in three dimensions. Tangential-normal continuity is introduced in order to develop distributional finite element curl div complexes. The spaces constructed are applied to discretize the quad curl problem, demonstrating optimal order of convergence. Furthermore, a hybridization technique is proposed, demonstrating its equivalence to nonconforming finite elements and weak Galerkin methods.