High-order accurate, entropy stable numerical methods for hyperbolic conservation laws have attracted much interest over the last decade, but only a few rigorous convergence results are available, particularly in multiple space dimensions. In this paper we show how the entropy stability of one such method, which is semi-discrete in time, yields a (weak) bound on oscillations. Under the assumption of L∞-boundedness of the approximations we use compensated compactness to prove convergence to a weak solution satisfying at least one entropy condition.
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Publié le :
DOI : 10.1051/m2an/2019090
Keywords: Multi-dimensional conservation laws, finite volume methods, TECNO scheme, entropy stability
@article{M2AN_2020__54_4_1415_0,
author = {Chatterjee, Neelabja and Fjordholm, Ulrik Skre},
title = {Convergence of second-order, entropy stable methods for multi-dimensional conservation laws},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1415--1428},
year = {2020},
publisher = {EDP Sciences},
volume = {54},
number = {4},
doi = {10.1051/m2an/2019090},
mrnumber = {4113056},
zbl = {1446.65088},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2019090/}
}
TY - JOUR AU - Chatterjee, Neelabja AU - Fjordholm, Ulrik Skre TI - Convergence of second-order, entropy stable methods for multi-dimensional conservation laws JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2020 SP - 1415 EP - 1428 VL - 54 IS - 4 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2019090/ DO - 10.1051/m2an/2019090 LA - en ID - M2AN_2020__54_4_1415_0 ER -
%0 Journal Article %A Chatterjee, Neelabja %A Fjordholm, Ulrik Skre %T Convergence of second-order, entropy stable methods for multi-dimensional conservation laws %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2020 %P 1415-1428 %V 54 %N 4 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2019090/ %R 10.1051/m2an/2019090 %G en %F M2AN_2020__54_4_1415_0
Chatterjee, Neelabja; Fjordholm, Ulrik Skre. Convergence of second-order, entropy stable methods for multi-dimensional conservation laws. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 4, pp. 1415-1428. doi: 10.1051/m2an/2019090
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