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Unconditional convergence and error estimates for bounded numerical solutions of the barotropic Navier–Stokes system
Author(s) -
Feireisl Eduard,
Hošek Radim,
Maltese David,
Novotný Antonín
Publication year - 2017
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22140
Subject(s) - barotropic fluid , mathematics , bounded function , discretization , mathematical analysis , smoothness , convergence (economics) , finite element method , domain (mathematical analysis) , a priori and a posteriori , limit (mathematics) , compressibility , physics , mechanics , philosophy , epistemology , economics , thermodynamics , economic growth
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 Δ t and the parameter h of the spatial discretization are proportional, Δ t ≈ h ; and (c) the family of numerical densities remains bounded for Δ t , h → 0 . No a priori smoothness is required for the limit (exact) solution. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1208–1223, 2017