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Error estimates of the Godunov method for the multidimensional compressible Euler system
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SYSNO ASEP 0557842 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Error estimates of the Godunov method for the multidimensional compressible Euler system Tvůrce(i) Lukáčová-Medviďová, M. (DE)
She, Bangwei (MU-W) SAI, RID, ORCID
Yuan, Y. (DE)Číslo článku 71 Zdroj.dok. Journal of Scientific Computing. - : Springer - ISSN 0885-7474
Roč. 91, č. 3 (2022)Poč.str. 27 s. Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova compressible Euler system ; consistency formulation ; error estimates ; Godunov method Vědní obor RIV BA - Obecná matematika Obor OECD Pure mathematics CEP GA21-02411S GA ČR - Grantová agentura ČR Způsob publikování Open access Institucionální podpora MU-W - RVO:67985840 UT WOS 000787294100001 EID SCOPUS 85128890283 DOI 10.1007/s10915-022-01843-6 Anotace 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. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2023 Elektronická adresa https://doi.org/10.1007/s10915-022-01843-6
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