Unconditional convergence and error estimates for bounded numerical solutions of the barotropic Navier–Stokes system |
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| Authors: | Eduard Feireisl Radim Ho?ek David Maltese Antonín Novotný |
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| Institution: | 1. Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic;2. Institut Mathématiques de Toulon, University of Toulon, La Garde, France |
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| 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  and the parameter  of the spatial discretization are proportional,  ; and (c) the family of numerical densities remains bounded for  . No a priori smoothness is required for the limit (exact) solution. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1208–1223, 2017 |
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| Keywords: | convergence error estimates mixed numerical method Navier– Stokes system |
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and the parameter 
of the spatial discretization are proportional, 
; and (c) the family of numerical densities remains bounded for 
. No a priori smoothness is required for the limit (exact) solution. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1208–1223, 2017