| Issue |
ESAIM: M2AN
Volume 57, Number 2, March-April 2023
|
|
|---|---|---|
| Page(s) | 395 - 422 | |
| DOI | https://doi.org/10.1051/m2an/2022092 | |
| Published online | 03 March 2023 | |
Quadratic stability of flux limiters
1
Laboratoire Jacques-Louis Lions, Sorbonne Université, 4 place Jussieu, 75005 Paris, France
2
Institut Universitaire de France, Paris, France
* Corresponding author: despres@ann.jussieu.fr
Received:
8
July
2022
Accepted:
9
November
2022
We propose a novel approach to study the quadratic stability of 2D flux limiters for non expansive transport equations. The theory is developed for the constant coefficient case on a cartesian grid. The convergence of the fully discrete nonlinear scheme is established in 2D with a rate not less than O(Δx½) in quadratic norm. It is a way to bypass the Goodman–Leveque obstruction Theorem. A new nonlinear scheme with corner correction is proposed. The scheme is formally second-order accurate away from characteristics points, satisfies the maximum principle and is proved to be convergent in quadratic norm. It is tested on simple numerical problems.
Mathematics Subject Classification: 65M08 / 65M12
Key words: Flux limiters / quadratic stability / quadratic convergence / Goodman–Leveque Theorem
© The authors. Published by EDP Sciences, SMAI 2023
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.