Volume 55, 2021Regular 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
|Page(s)||S573 - S591|
|Published online||26 February 2021|
Convergence of an implicit scheme for diagonal non-conservative hyperbolic systems
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: firstname.lastname@example.org
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
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.