A least squares Petrov-Galerkin finite element method for the stationary Navier-Stokes equations

Authors:
Tian Xiao Zhou and Min Fu Feng

Journal:
Math. Comp. **60** (1993), 531-543

MSC:
Primary 65N30; Secondary 76D05, 76M10

DOI:
https://doi.org/10.1090/S0025-5718-1993-1164127-6

MathSciNet review:
1164127

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Abstract: In this paper, a Galerkin/least squares-type finite element method is proposed and analyzed for the stationary Navier-Stokes equations. The method is consistent and stable for any combination of discrete velocity and pressure spaces (without requiring a Babuška-Brezzi stability condition). The existence, uniqueness and convergence (at optimal rate) of the discrete solution is proved in the case of sufficient viscosity (or small data).

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DOI:
https://doi.org/10.1090/S0025-5718-1993-1164127-6

Article copyright:
© Copyright 1993
American Mathematical Society