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.
Keywords: Implicit upwind scheme, diagonal non-conservative hyperbolic systems, transport systems, discrete gradient estimates, monotone discrete solutions, Lipschitz discrete solutions
@article{M2AN_2021__55_S1_S573_0,
author = {Boudjerada, Rachida and El Hajj, Ahmad and Oussaily, Aya},
title = {Convergence of an implicit scheme for diagonal non-conservative hyperbolic systems},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {S573--S591},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {Suppl\'ement},
doi = {10.1051/m2an/2020049},
mrnumber = {4221324},
zbl = {1501.65028},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2020049/}
}
TY - JOUR AU - Boudjerada, Rachida AU - El Hajj, Ahmad AU - Oussaily, Aya TI - Convergence of an implicit scheme for diagonal non-conservative hyperbolic systems JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - S573 EP - S591 VL - 55 IS - Supplément PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2020049/ DO - 10.1051/m2an/2020049 LA - en ID - M2AN_2021__55_S1_S573_0 ER -
%0 Journal Article %A Boudjerada, Rachida %A El Hajj, Ahmad %A Oussaily, Aya %T Convergence of an implicit scheme for diagonal non-conservative hyperbolic systems %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P S573-S591 %V 55 %N Supplément %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2020049/ %R 10.1051/m2an/2020049 %G en %F M2AN_2021__55_S1_S573_0
Boudjerada, Rachida; El Hajj, Ahmad; Oussaily, Aya. Convergence of an implicit scheme for diagonal non-conservative hyperbolic systems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021), pp. S573-S591. doi: 10.1051/m2an/2020049
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