A local discontinuous Galerkin approximation for systems with p-structure

In the present paper, we propose a local discontinuous Galerkin (LDG) approximation for systems with p-structure. We discuss appropriate DG spaces and numerical fluxes for the problem. Based on the primal formulation, we show stability (a priori estimates) of the method. We derive error estimates, which are optimal for linear ansatz functions. Moreover, we prove new functional analytic tools for the DG setting.