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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

  • Czech description

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