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

TL;DR

This paper analyzes the convergence of a Local Discontinuous Galerkin method for nonlinear systems with balanced Orlicz-structure, introducing a new flux that achieves optimal rates across various problem types.

Contribution

It presents a novel numerical flux for LDG methods that ensures optimal convergence for systems with balanced Orlicz-structure, unifying treatment for different $(p, abla)$-structures.

Findings

Achieves optimal convergence rates for linear ansatz functions.

Provides a unified approach for $(p, abla)$-structure problems.

Introduces a new numerical flux for LDG methods.

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 $(p,\delta)$-structure for arbitrary $p \in (1,\infty)$ and $\delta\ge 0$.