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

Abstract

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, δ)-structure for arbitrary p ∈ (1, ∞) and δ ≥ 0.