Discontinuous Galerkin methods for the p-biharmonic equation from a discrete variational perspective

We study discontinuous Galerkin approximations of the p-biharmonic equation for p ∈ (1, ∞) from a variational perspective. We propose a discrete variational formulation of the problem based on an appropriate definition of a finite element Hessian and study convergence of the method (without rates) using a semicontinuity argument. We also present numerical experiments aimed at testing the robustness of the method.