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# Asymptotic preserving error estimates for numerical solutions of compressible Navier-Stokes equations in the low Mach number regime

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SYSNO ASEP 0485868 J - Článek v odborném periodiku J - Článek v odborném periodiku Článek ve WOS Asymptotic preserving error estimates for numerical solutions of compressible Navier-Stokes equations in the low Mach number regime Feireisl, Eduard (MU-W) RID, SAI, ORCID Lukáčová-Medviďová, M. (DE) Nečasová, Šárka (MU-W) RID, SAI, ORCID Novotný, A. (FR) She, Bangwei (MU-W) SAI, RID, ORCID Multiscale Modeling and Simulation - ISSN 1540-3459 Roč. 16, č. 1 (2018), s. 150-183 34 s. eng - angličtina US - Spojené státy americké Navier-Stokes system ; finite element numerical method ; finite volume numerical method ; asymptotic preserving schemes BA - Obecná matematika Pure mathematics GA16-03230S GA ČR - Grantová agentura ČR MU-W - RVO:67985840 000429645500006 85045026178 10.1137/16M1094233 We study the convergence of numerical solutions of the compressible Navier-Stokes system to its incompressible limit. The numerical solution is obtained by a combined finite element-finite volume method based on the linear Crouzeix-Raviart finite element for the velocity and piecewise constant approximation for the density. The convective terms are approximated using upwinding. The distance between a numerical solution of the compressible problem and the strong solution of the incompressible Navier-Stokes equations is measured by means of a relative energy functional. For barotropic pressure exponent $\gamma \geq 3/2$ and for well-prepared initial data we obtain uniform convergence of order $\cal O(\sqrt\Delta t, h^a, \varepsilon)$, $a = \min \ \frac{2 \gamma - 3 \gamma, 1\$. Extensive numerical simulations confirm that the numerical solution of the compressible problem converges to the solution of the incompressible Navier-Stokes equations as the discretization parameters $\Delta t$, $h$ and the Mach number $\varepsilon$ tend to zero. Matematický ústav Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 2019
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