  We want to propose a new discretization ansatz for the second order Hessian
complex exploiting benefits of isogeometric analysis, namely the possibility of
high-order convergence and smoothness of test functions. Although our approach
is firstly only valid in domains that are obtained by affine linear
transformations of a unit cube, we see in the approach a relatively simple way
to obtain inf-sup stable and arbitrary fast convergent methods for the
underlying Hodge-Laplacians. Background for this is the theory of Finite
Element Exterior Calculus (FEEC) which guides us to structure-preserving
discrete sub-complexes.
