Volume 57, Number 2, March-April 2023
|Page(s)||395 - 422|
|Published online||03 March 2023|
Quadratic stability of flux limiters
Laboratoire Jacques-Louis Lions, Sorbonne Université, 4 place Jussieu, 75005 Paris, France
2 Institut Universitaire de France, Paris, France
* Corresponding author: email@example.com
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.
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