Gutenberg Open Science: Error estimates of the Godunov method for the multidimensional compressible Euler system

Please use this identifier to cite or link to this item: http://doi.org/10.25358/openscience-8321

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DC Field	Value	Language
dc.contributor.author	Lukáčová-Medvid’ová, Mária	-
dc.contributor.author	She, Bangwei	-
dc.contributor.author	Yuan, Yuhuan	-
dc.date.accessioned	2022-12-15T09:43:34Z	-
dc.date.available	2022-12-15T09:43:34Z	-
dc.date.issued	2022	-
dc.identifier.uri	https://openscience.ub.uni-mainz.de/handle/20.500.12030/8337	-
dc.description.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.	en_GB
dc.description.sponsorship	Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 491381577	de
dc.language.iso	eng	de
dc.rights	CC BY	*
dc.rights.uri	https://creativecommons.org/licenses/by/4.0/	*
dc.subject.ddc	510 Mathematik	de_DE
dc.subject.ddc	510 Mathematics	en_GB
dc.title	Error estimates of the Godunov method for the multidimensional compressible Euler system	en_GB
dc.type	Zeitschriftenaufsatz	de
dc.identifier.doi	http://doi.org/10.25358/openscience-8321	-
jgu.type.dinitype	article	en_GB
jgu.type.version	Published version	de
jgu.type.resource	Text	de
jgu.organisation.department	FB 08 Physik, Mathematik u. Informatik	de
jgu.organisation.number	7940	-
jgu.organisation.name	Johannes Gutenberg-Universität Mainz	-
jgu.rights.accessrights	openAccess	-
jgu.journal.title	Journal of scientific computing	de
jgu.journal.volume	91	de
jgu.pages.alternative	71	de
jgu.publisher.year	2022	-
jgu.publisher.name	Springer Science + Business Media B.V.	de
jgu.publisher.place	New York, NY	de
jgu.publisher.issn	1573-7691	de
jgu.organisation.place	Mainz	-
jgu.subject.ddccode	510	de
jgu.publisher.doi	10.1007/s10915-022-01843-6	de
jgu.organisation.ror	https://ror.org/023b0x485	-
jgu.subject.dfg	Naturwissenschaften	de
Appears in collections:	DFG-491381577-H

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