Convergence and error estimates for a finite difference scheme for the multi-dimensional compressible Navier-Stokes system

0531380 - MÚ 2021 RIV US eng J - Journal Article
Mizerová, Hana - She, Bangwei
Convergence and error estimates for a finite difference scheme for the multi-dimensional compressible Navier-Stokes system.
Journal of Scientific Computing. Roč. 84, č. 1 (2020), č. článku 25. ISSN 0885-7474. E-ISSN 1573-7691
R&D Projects: GA ČR(CZ) GA18-05974S
Institutional support: RVO:67985840
Keywords : compressible Navier–Stokes system * convergence * error estimates * finite difference method
OECD category: Applied mathematics
Impact factor: 2.592, year: 2020
Method of publishing: Limited access
https://doi.org/10.1007/s10915-020-01278-x

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.
Permanent Link: http://hdl.handle.net/11104/0310039