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

Zhou, Tian Xiao; Feng, Min Fu

doi:10.1090/S0025-5718-1993-1164127-6

A least squares Petrov-Galerkin finite element method for the stationary Navier-Stokes equations
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by Tian Xiao Zhou and Min Fu Feng PDF

Math. Comp. 60 (1993), 531-543 Request permission

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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Application to the advective-diffusion model