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: email@example.com
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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