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

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