  Several smooth finite element de Rham complexes are constructed in
three-dimensional space, which yield three families of grad-div conforming
finite elements. The simplest element has only 8 degrees of freedom (DOFs) for
a tetrahedron and 14 DOFs for a cuboid. These elements naturally lead to
conforming approximations to quad-div problems. Numerical experiments for each
family validate the correctness and efficiency of the elements for solving the
quad-div problem.

Numerical Analysis;Numerical Analysis