Improved error estimates for the finite volume and the MAC schemes for the compressible Navier-Stokes system

0569931 - MÚ 2024 RIV DE eng J - Journal Article
Feireisl, Eduard - Lukáčová-Medviďová, M. - She, Bangwei
Improved error estimates for the finite volume and the MAC schemes for the compressible Navier-Stokes system.
Numerische Mathematik. Roč. 153, 2-3 (2023), s. 493-529. ISSN 0029-599X. E-ISSN 0945-3245
R&D Projects: GA ČR(CZ) GA21-02411S
Institutional support: RVO:67985840
Keywords : difference scheme * element-method * convergence
OECD category: Pure mathematics
Impact factor: 2.1, year: 2022
Method of publishing: Open access
https://doi.org/10.1007/s00211-023-01346-y

We present new error estimates for the finite volume and finite difference methods applied to the compressible Navier–Stokes equations. The main innovative ingredients of the improved error estimates are a refined consistency analysis combined with a continuous version of the relative energy inequality. Consequently, we obtain better convergence rates than those available in the literature so far. Moreover, the error estimates hold in the whole physically relevant range of the adiabatic coefficient.
Permanent Link: https://hdl.handle.net/11104/0341249