Convergence of a mixed finite element finite volume scheme for the isentropic Navier-Stokes system via dissipative measure-valued solutions

0489965 - MÚ 2019 RIV US eng J - Journal Article
Feireisl, Eduard - Lukáčová-Medviďová, M.
Convergence of a mixed finite element finite volume scheme for the isentropic Navier-Stokes system via dissipative measure-valued solutions.
Foundations of Computational Mathematics. Roč. 18, č. 3 (2018), s. 703-730. ISSN 1615-3375. E-ISSN 1615-3383
EU Projects: European Commission(XE) 320078 - MATHEF
Institutional support: RVO:67985840
Keywords : compressible Navier-Stokes system * finite volume scheme * finite element scheme
OECD category: Applied mathematics
Impact factor: 2.540, year: 2018
https://link.springer.com/article/10.1007%2Fs10208-017-9351-2

We study convergence of a mixed finite element–finite volume numerical scheme for the isentropic Navier–Stokes system under the full range of the adiabatic exponent. We establish suitable stability and consistency estimates and show that the Young measure generated by numerical solutions represents a dissipative measure-valued solutions of the limit system. In particular, using the recently established weak–strong uniqueness principle in the class of dissipative measure-valued solutions we show that the numerical solutions converge strongly to a strong solutions of the limit system as long as the latter exists.
Permanent Link: http://hdl.handle.net/11104/0284257