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

04/21/2022
by   Alex Kaltenbach, et al.
0

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,δ)-structure for arbitrary p ∈ (1,∞) and δ≥ 0, our approach yields a unified treatment.

READ FULL TEXT

page 21

page 22

08/08/2022

A Local Discontinuous Galerkin approximation for the p-Navier-Stokes system, Part II: Convergence rates for the velocity

In the present paper, we prove convergence rates for the Local Discontin...
12/21/2020

A p-robust polygonal discontinuous Galerkin method with minus one stabilization

We introduce a new stabilization for discontinuous Galerkin methods for ...
09/19/2022

Superconvergence of discontinuous Petrov-Galerkin approximations in linear elasticity

Existing a priori convergence results of the discontinuous Petrov-Galerk...
08/08/2022

A Local Discontinuous Galerkin approximation for the p-Navier-Stokes system, Part I: Convergence analysis

In the present paper, we propose a Local Discontinuous Galerkin (LDG) ap...
02/08/2021

Approximation of discontinuous functions by Kantorovich exponential sampling series

The Kantorovich exponential sampling series at jump discontinuities of t...
02/27/2020

Structure aware Runge-Kutta time stepping for spacetime tents

We introduce a new class of Runge-Kutta type methods suitable for time s...
09/14/2020

Analysis of a mixed discontinuous Galerkin method for the time-harmonic Maxwell equations with minimal smoothness requirements

An error analysis of a mixed discontinuous Galerkin (DG) method with Bre...