Issue |
ESAIM: M2AN
Volume 58, Number 5, September-October 2024
|
|
---|---|---|
Page(s) | 1907 - 1933 | |
DOI | https://doi.org/10.1051/m2an/2024051 | |
Published online | 10 October 2024 |
Note on quasi-optimal error estimates for the pressure for shear-thickening fluids
1
Institute of Mathematics, Technical University of Berlin, Straße des 17. Juni 135, 10623 Berlin, Germany
2
Department of Applied Mathematics, University of Freiburg, Ernst–Zermelo-Straße 1, 79104 Freiburg, Germany
* Corresponding author: kaltenbach@math.tu-berlin.de
Received:
5
February
2024
Accepted:
21
June
2024
In this paper, we derive quasi-optimal a priori error estimates for the kinematic pressure for a Local Discontinuous Galerkin (LDG) approximation of steady systems of p-Navier–Stokes type in the case of shear-thickening, i.e., p > 2, imposing a new Muckenhoupt regularity condition on the viscosity of the fluid, which is mild in the two-dimensional case but potentially restrictive in the three-dimensional case.
Mathematics Subject Classification: 76A05 / 35Q35 / 65N30 / 65N15
Key words: Discontinuous Galerkin method / p-Navier–Stokes system / pressure / a priori error estimate / Muckenhoupt weights
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.