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