A Local Discontinuous Galerkin approximation for the $p$-Navier-Stokes system, Part III: Convergence rates for the pressure

TL;DR

This paper establishes convergence rates for the pressure in a Local Discontinuous Galerkin method applied to p-Navier-Stokes systems, supported by numerical experiments, advancing numerical analysis in non-Newtonian fluid dynamics.

Contribution

It provides the first rigorous convergence rate analysis for the pressure in LDG approximations of p-Navier-Stokes systems for p>2.

Findings

Proved convergence rates for pressure in LDG methods.

Numerical experiments confirm theoretical results.

Enhanced understanding of numerical approximation for non-Newtonian flows.

Abstract

In the present paper, we prove convergence rates for the pressure of the Local Discontinuous Galerkin (LDG) approximation, proposed in Part I of the paper, of systems of $p$-Navier-Stokes type and $p$-Stokes type with $p\in (2,\infty)$. The results are supported by numerical experiments.