  The Tangential-Displacement Normal-Normal-Stress (TDNNS) method is a finite
element method for mixed elasticity. As the name suggests, the tangential
component of the displacement vector as well as the normal-normal component of
the stress are the degrees of freedom of the finite elements. The TDNNS method
was shown to converge of optimal order, and to be robust with respect to shear
and volume locking. However, the method is slightly nonconforming, and an
analysis with respect to the natural norms of the arising spaces was still
missing. We present a sound mathematical theory of the infinite dimensional
problem using the space H(curl) for the displacement. We define the space H(div
div) for the stresses and provide trace operators for the normal-normal stress.
Moreover, the finite element problem is shown to be stable with respect to the
H(curl) and a discrete H(div div) norm. A-priori error estimates of optimal
order with respect to these norms are obtained.
