  A unified construction of $H(\textrm{div})$-conforming finite element
tensors, including vector div element, symmetric div matrix element, traceless
div matrix element, and in general tensors with linear constraints, is
developed in this work. It is based on the geometric decomposition of Lagrange
elements into bubble functions on each sub-simplex. Then the tensor at each
sub-simplex is decomposed into the tangential and the normal component. The
tangential component forms the bubble function space and the normal component
characterizes the trace. A deep exploration on boundary degrees of freedom is
presented for discovering various finite elements. The developed finite element
spaces are $H(\textrm{div})$-conforming and satisfy the discrete inf-sup
condition. An explicit basis of the constraint tensor space is also
established.
