Convergence analysis of a Local Discontinuous Galerkin approximation for nonlinear systems with Orlicz-structure

In this paper, we investigate a Local Discontinuous Galerkin (LDG) approximation for systems with Orlicz-structure. We propose a new numerical flux, which yields optimal convergence rates for linear ansatz functions. In particular, for problems with $(p,\delta)$-structure for arbitrary $p \in (1,\infty)$ and $\delta\ge 0$, our approach yields a unified treatment.