Unconditional convergence and error estimates for bounded numerical solutions of the barotropic Navier–Stokes system | Zendy

Feireisl Eduard | Zendy; Hošek Radim | Zendy; Maltese David | Zendy; Novotný Antonín | Zendy

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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

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