Unconditional convergence and error estimates for bounded numerical solutions of the barotropic Navier-Stokes system

0474208 - MÚ 2018 RIV US eng J - Journal Article
Feireisl, Eduard - Hošek, Radim - Maltese, D. - Novotný, A.
Unconditional convergence and error estimates for bounded numerical solutions of the barotropic Navier-Stokes system.
Numerical Methods for Partial Differential Equations. Roč. 33, č. 4 (2017), s. 1208-1223. ISSN 0749-159X. E-ISSN 1098-2426
EU Projects: European Commission(XE) 320078 - MATHEF
Institutional support: RVO:67985840
Keywords : convergence * error estimates * mixed numerical method * Navier–Stokes system
OECD category: Pure mathematics
Impact factor: 1.305, year: 2017
http://onlinelibrary.wiley.com/doi/10.1002/num.22140/abstract

We consider a mixed finite-volume finite-element method applied to the Navier-Stokes system of equations describing the motion of a compressible, barotropic, viscous fluid. We show convergence as well as error estimates for the family of numerical solutions on condition that: (a) the underlying physical domain as well as the data are smooth, (b) the time step math formula and the parameter math formula of the spatial discretization are proportional, math formula, and (c) the family of numerical densities remains bounded for math formula. No a priori smoothness is required for the limit (exact) solution.
Permanent Link: http://hdl.handle.net/11104/0271328