  We study discontinuous Galerkin approximations of the $p$--biharmonic
equation from a variational perspective. We propose a discrete variational
formulation of the problem based on a appropriate definition of a finite
element Hessian and study convergence of the method (without rates) using a
weak lower semicontinuity argument.
  We present numerical experiments aimed at testing the robustness of the
method. We also note a superconvergence effect for some values of $p$.
