Conditional quasi-optimal error estimate for a finite element discretization of the $p$-Navier-Stokes equations: The case $p>2$

TL;DR

This paper establishes quasi-optimal error estimates for finite element approximations of the steady p-Navier-Stokes equations in shear-thickening fluids, under a new regularity condition, advancing numerical analysis in non-Newtonian fluid modeling.

Contribution

It introduces a novel error estimation approach for the finite element discretization of p-Navier-Stokes equations with p>2, under a new Muckenhoupt regularity condition.

Findings

Derived quasi-optimal a priori error estimates for pressure

Applicable to shear-thickening fluids with p>2

Imposed a new mild Muckenhoupt regularity condition

Abstract

In this paper, we derive quasi-optimal $\textit{a priori}$ error estimates for the kinematic pressure for a Finite Element (FE) approximation of steady systems of $p$-Navier-Stokes type in the case of shear-thickening, $\textit{i.e.}$, in the case $p>2$, imposing a new mild Muckenhoupt regularity condition.