Error estimates of the Godunov method for the multidimensional compressible Euler system
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00557842" target="_blank" >RIV/67985840:_____/22:00557842 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s10915-022-01843-6" target="_blank" >https://doi.org/10.1007/s10915-022-01843-6</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10915-022-01843-6" target="_blank" >10.1007/s10915-022-01843-6</a>
Alternative languages
Result language
angličtina
Original language name
Error estimates of the Godunov method for the multidimensional compressible Euler system
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA21-02411S" target="_blank" >GA21-02411S: Solving ill posed problems in the dynamics of compressible fluids</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Scientific Computing
ISSN
0885-7474
e-ISSN
1573-7691
Volume of the periodical
91
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
27
Pages from-to
71
UT code for WoS article
000787294100001
EID of the result in the Scopus database
2-s2.0-85128890283