Please use this identifier to cite or link to this item:
http://doi.org/10.25358/openscience-8321
Authors: | Lukáčová-Medvid’ová, Mária She, Bangwei Yuan, Yuhuan |
Title: | Error estimates of the Godunov method for the multidimensional compressible Euler system |
Online publication date: | 15-Dec-2022 |
Year of first publication: | 2022 |
Language: | english |
Abstract: | We derive a priori error estimates of the Godunov method for the multidimensional compressible Euler system of gas dynamics. To this end we apply the relative energy principle and estimate the distance between the numerical solution and the strong solution. This yields also the estimates of the L2-norms of the errors in density, momentum and entropy. Under the assumption, that the numerical density is uniformly bounded from below by a positive constant and that the energy is uniformly bounded from above and stays positive, we obtain a convergence rate of 1/2 for the relative energy in the L1-norm, that is to say, a convergence rate of 1/4 for the L2-error of the numerical solution. Further, under the assumption—the total variation of the numerical solution is uniformly bounded, we obtain the first order convergence rate for the relative energy in the L1-norm, consequently, the numerical solution converges in the L2-norm with the convergence rate of 1/2. The numerical results presented are consistent with our theoretical analysis. |
DDC: | 510 Mathematik 510 Mathematics |
Institution: | Johannes Gutenberg-Universität Mainz |
Department: | FB 08 Physik, Mathematik u. Informatik |
Place: | Mainz |
ROR: | https://ror.org/023b0x485 |
DOI: | http://doi.org/10.25358/openscience-8321 |
Version: | Published version |
Publication type: | Zeitschriftenaufsatz |
License: | CC BY |
Information on rights of use: | https://creativecommons.org/licenses/by/4.0/ |
Journal: | Journal of scientific computing 91 |
Pages or article number: | 71 |
Publisher: | Springer Science + Business Media B.V. |
Publisher place: | New York, NY |
Issue date: | 2022 |
ISSN: | 1573-7691 |
Publisher DOI: | 10.1007/s10915-022-01843-6 |
Appears in collections: | DFG-491381577-H |
Files in This Item:
File | Description | Size | Format | ||
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error_estimates_of_the_goduno-20221117134004290.pdf | 1.26 MB | Adobe PDF | View/Open |