@inproceedings{281a20eec4f24d87bb6f43adf4528bf2,
title = "On the accuracy of finite-difference schemes in smooth parts of calculated weak solutions",
abstract = "We consider explicit two-layer in time finite-difference schemes intended for the shock capturing calculation of weak solutions of quasilinear hyperbolic systems of conservation laws. The accuracy of these schemes in the areas of smoothness of the calculated weak solution is studied. It is shown that in these regions the errors of the difference solution approximately satisfy the hyperbolic system of differential equations, which have characteristics fields that are the same as the approximated system of conservation laws. This implies that in the shock influence region the convergence rate of the difference solution essentially depends on the accuracy with which the scheme approximates the Hugoniot conditions at the shock front. This explains the decrease in the convergence order of NFC (Nonlinear Flux Correction) schemes in the shock influence regions.",
author = "Olyana Kovyrkina and Vladimir Ostapenko",
note = "Funding Information: The work was carried out with support by the Russian Science Foundation (grant No. 16-11-10033). Publisher Copyright: {\textcopyright} 2020 American Institute of Physics Inc.. All rights reserved. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.; International Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019 ; Conference date: 23-09-2019 Through 28-09-2019",
year = "2020",
month = nov,
day = "24",
doi = "10.1063/5.0026831",
language = "English",
series = "AIP Conference Proceedings",
publisher = "American Institute of Physics Inc.",
editor = "Simos, {Theodore E.} and Charalambos Tsitouras",
booktitle = "International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019",
}