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

Abstract

In this paper, we derive quasi-optimal $\text{a priori}$ 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, $\text{i.e.}$, in the case $p>2$, imposing a new mild Muckenhoupt regularity condition.

20 pages, 3 figures, 6 tables. arXiv admin note: substantial text overlap with arXiv:2402.03056