| Issue |
ESAIM: M2AN
Volume 55, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
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|---|---|---|
| Page(s) | S573 - S591 | |
| DOI | https://doi.org/10.1051/m2an/2020049 | |
| Published online | 26 February 2021 | |
Convergence of an implicit scheme for diagonal non-conservative hyperbolic systems
1
USTHB, Faculté de Mathématiques, Laboratory AMNEDP, BP32 El Alia, Bab Ezzouar, Alger, Algérie
2
Sorbonne Universités, Université de Technologie de Compiègne, LMAC, 60205 Compiègne Cedex, France
* Corresponding author: elhajjah@utc.fr
Received:
11
February
2020
Accepted:
13
July
2020
In this paper, we consider diagonal non-conservative hyperbolic systems in one space dimension with monotone and large Lipschitz continuous data. Under a certain nonnegativity condition on the Jacobian matrix of the velocity of the system, global existence and uniqueness results of a Lipschitz solution for this system, which is not necessarily strictly hyperbolic, was proved in El Hajj and Monneau (J. Hyperbolic Differ. Equ. 10 (2013) 461–494). We propose a natural implicit scheme satisfiying a similar Lipschitz estimate at the discrete level. This property allows us to prove the convergence of the scheme without assuming it strictly hyperbolic.
Mathematics Subject Classification: 35A01 / 74G25 / 35F20 / 35F21 / 70H20 / 35Q74
Key words: Implicit upwind scheme / diagonal non-conservative hyperbolic systems / transport systems / discrete gradient estimates / monotone discrete solutions / Lipschitz discrete solutions
© EDP Sciences, SMAI 2021
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