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An optimal order error estimate for an upwind discretization of the Navier—Stokes equations
Author(s) -
Schieweck F.,
Tobiska L.
Publication year - 1996
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/(sici)1098-2426(199607)12:4<407::aid-num1>3.0.co;2-q
Subject(s) - mathematics , discretization , norm (philosophy) , finite element method , upwind scheme , compressibility , navier–stokes equations , mathematical analysis , pressure correction method , mechanics , physics , political science , law , thermodynamics
We analyze a finite‐element approximation of the stationary incompressible Navier–Stokes equations in primitive variables. This approximation is based on the nonconforming P 1 / P 0 element pair of Crouzeix/Raviart and a special upwind discretization of the convective term. An optimal error estimate in a discrete H 1 ‐norm for the velocity and in the L 2 ‐norm for the pressure is proved. Some numerical results are presented. © 1996 John Wiley & Sons, Inc.