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].
Mots-clés : Navier–Stokes system, finite element numerical method, finite volume numerical method, error estimates
@article{M2AN_2017__51_1_279_0, author = {Feireisl, Eduard and Ho\v{s}ek, Radim and Maltese, David and Novotn\'y, Anton{\'\i}n}, title = {Error estimates for a numerical method for the compressible {Navier{\textendash}Stokes} system on sufficiently smooth domains}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {279--319}, publisher = {EDP-Sciences}, volume = {51}, number = {1}, year = {2017}, doi = {10.1051/m2an/2016022}, zbl = {1360.35144}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/m2an/2016022/} }
TY - JOUR AU - Feireisl, Eduard AU - Hošek, Radim AU - Maltese, David AU - Novotný, Antonín TI - Error estimates for a numerical method for the compressible Navier–Stokes system on sufficiently smooth domains JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 279 EP - 319 VL - 51 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2016022/ DO - 10.1051/m2an/2016022 LA - en ID - M2AN_2017__51_1_279_0 ER -
%0 Journal Article %A Feireisl, Eduard %A Hošek, Radim %A Maltese, David %A Novotný, Antonín %T Error estimates for a numerical method for the compressible Navier–Stokes system on sufficiently smooth domains %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 279-319 %V 51 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2016022/ %R 10.1051/m2an/2016022 %G en %F M2AN_2017__51_1_279_0
Feireisl, Eduard; Hošek, Radim; Maltese, David; Novotný, Antonín. Error estimates for a numerical method for the compressible Navier–Stokes system on sufficiently smooth domains. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 1, pp. 279-319. doi : 10.1051/m2an/2016022. http://archive.numdam.org/articles/10.1051/m2an/2016022/
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