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Convergence and error estimates for a finite difference scheme for the multi-dimensional compressible Navier-Stokes system
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SYSNO ASEP 0531380 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Convergence and error estimates for a finite difference scheme for the multi-dimensional compressible Navier-Stokes system Author(s) Mizerová, Hana (MU-W) SAI, RID
She, Bangwei (MU-W) SAI, RID, ORCIDArticle number 25 Source Title Journal of Scientific Computing. - : Springer - ISSN 0885-7474
Roč. 84, č. 1 (2020)Number of pages 39 s. Language eng - English Country US - United States Keywords compressible Navier–Stokes system ; convergence ; error estimates ; finite difference method Subject RIV BA - General Mathematics OECD category Applied mathematics R&D Projects GA18-05974S GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000552410600003 EID SCOPUS 85088154081 DOI 10.1007/s10915-020-01278-x Annotation We prove convergence of a finite difference approximation of the compressible Navier–Stokes system towards the strong solution in Rd, d= 2 , 3 , for the adiabatic coefficient γ> 1. Employing the relative energy functional, we find a convergence rate which is uniform in terms of the discretization parameters for γ> d/ 2. All results are unconditional in the sense that we have no assumptions on the regularity nor boundedness of the numerical solution. We also provide numerical experiments to validate the theoretical convergence rate. To the best of our knowledge this work contains the first unconditional result on the convergence of a finite difference scheme for the unsteady compressible Navier–Stokes system in multiple dimensions. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2021 Electronic address https://doi.org/10.1007/s10915-020-01278-x
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