Error Estimates of the Godunov Method for the Multidimensional Compressible Euler System

Publication type:
Journal article
Metadata:
Autoren
  • Maria Lukacova-Medvid'ova
  • Bangwei She
  • Yuhuan Yuan
Autoren-URL
https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=fis-test-1&SrcAuth=WosAPI&KeyUT=WOS:000787294100001&DestLinkType=FullRecord&DestApp=WOS_CPL
DOI
10.1007/s10915-022-01843-6
eISSN
1573-7691
Externe Identifier
  • Clarivate Analytics Document Solution ID: 0T9PW
ISSN
0885-7474
Ausgabe der Veröffentlichung
3
Zeitschrift
JOURNAL OF SCIENTIFIC COMPUTING
Schlüsselwörter
  • Compressible Euler system
  • Error estimates
  • Relative energy
  • Godunov method
  • Consistency formulation
  • Strong solution
Artikelnummer
ARTN 71
Datum der Veröffentlichung
2022
Status
Published
Titel
Error Estimates of the Godunov Method for the Multidimensional Compressible Euler System
Sub types
  • Article
Ausgabe der Zeitschrift
91

Data source: Web of Science (Lite)

Other metadata sources:
Abstract
<jats:title>Abstract</jats:title><jats:p>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<jats:inline-formula><jats:alternatives><jats:tex-math>$$L^2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>L</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math></jats:alternatives></jats:inline-formula>-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<jats:inline-formula><jats:alternatives><jats:tex-math>$$L^1$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>L</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:math></jats:alternatives></jats:inline-formula>-norm, that is to say, a convergence rate of 1/4 for the<jats:inline-formula><jats:alternatives><jats:tex-math>$$L^2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>L</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math></jats:alternatives></jats:inline-formula>-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<jats:inline-formula><jats:alternatives><jats:tex-math>$$L^1$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>L</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:math></jats:alternatives></jats:inline-formula>-norm, consequently, the numerical solution converges in the<jats:inline-formula><jats:alternatives><jats:tex-math>$$L^2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>L</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math></jats:alternatives></jats:inline-formula>-norm with the convergence rate of 1/2. The numerical results presented are consistent with our theoretical analysis.</jats:p>
Autoren
  • Mária Lukáčová-Medvid’ová
  • Bangwei She
  • Yuhuan Yuan
DOI
10.1007/s10915-022-01843-6
eISSN
1573-7691
ISSN
0885-7474
Ausgabe der Veröffentlichung
3
Zeitschrift
Journal of Scientific Computing
Sprache
en
Artikelnummer
71
Online publication date
2022
Datum der Veröffentlichung
2022
Status
Published
Herausgeber
Springer Science and Business Media LLC
Herausgeber URL
http://dx.doi.org/10.1007/s10915-022-01843-6
Datum der Datenerfassung
2023
Titel
Error Estimates of the Godunov Method for the Multidimensional Compressible Euler System
Ausgabe der Zeitschrift
91

Data source: Crossref

Author's licence
CC-BY
Autoren
  • Mária Lukáčová-Medvid’ová
  • Bangwei She
  • Yuhuan Yuan
Hosting institution
Universitätsbibliothek Mainz
Sammlungen
  • DFG-491381577-H
Resource version
Published version
DOI
10.1007/s10915-022-01843-6
Funding acknowledgements
  • Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 491381577
File(s) embargoed
false
Open access
true
ISSN
1573-7691
Zeitschrift
Journal of scientific computing
Schlüsselwörter
  • 510 Mathematik
  • 510 Mathematics
Sprache
eng
Open access status
Open Access
Paginierung
71
Datum der Veröffentlichung
2022
Public URL
https://openscience.ub.uni-mainz.de/handle/20.500.12030/8337
Herausgeber
Springer Science + Business Media B.V.
Datum der Datenerfassung
2022
Datum, an dem der Datensatz öffentlich gemacht wurde
2022
Zugang
Public
Titel
Error estimates of the Godunov method for the multidimensional compressible Euler system
Ausgabe der Zeitschrift
91

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