Error estimates for a numerical method for the compressible Navier–Stokes system on sufficiently smooth domains

We derive an a priori error estimate for the numerical solution obtained by time and space discretization by the finite volume/finite element method of the barotropic Navier–Stokes equations. The numerical solution on a convenient polyhedral domain approximating a sufficiently smooth bounded domain...

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Bibliographic Details
Published in:ESAIM. Mathematical modelling and numerical analysis 2017-01, Vol.51 (1), p.279-319
Main Authors: Feireisl, Eduard, Hošek, Radim, Maltese, David, Novotný, Antonín
Format: Article
Language:English
Subjects:
35Q30
65N12
65N30
76M10
76M12
76N10
76N15
Analysis of PDEs
Compressibility
Computational fluid dynamics
Domains
error estimates
Finite element method
finite element numerical method
finite volume numerical method
Fluid flow
Mathematical analysis
Mathematics
Navier-Stokes equations
Navier–Stokes system
Numerical methods
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Summary:We derive an a priori error estimate for the numerical solution obtained by time and space discretization by the finite volume/finite element method of the barotropic Navier–Stokes equations. The numerical solution on a convenient polyhedral domain approximating a sufficiently smooth bounded domain is compared with an exact solution of the barotropic Navier–Stokes equations with a bounded density. The result is unconditional in the sense that there are no assumed bounds on the numerical solution. It is obtained by the combination of discrete relative energy inequality derived in [T. Gallouët, R. Herbin, D. Maltese and A. Novotný, IMA J. Numer. Anal. 36 (2016) 543–592.] and several recent results in the theory of compressible Navier–Stokes equations concerning blow up criterion established in [Y. Sun, C. Wang and Z. Zhang, J. Math. Pures Appl. 95 (2011) 36–47] and weak strong uniqueness principle established in [E. Feireisl, B.J. Jin and A. Novotný, J. Math. Fluid Mech. 14 (2012) 717–730].
ISSN:0764-583X
1290-3841
DOI:10.1051/m2an/2016022