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A nonconforming finite element method of upstream type applied to the stationary Navier-Stokes equation. (English) Zbl 0681.76032
Summary: We present a nonconforming finite element method with an upstream discretization of the convective terms for solving the stationary Navier- Stokes equations. The existence of at least one solution of the discrete problem and the convergence of subsequences of such solutions to a solution of the Navier-Stokes equations are established. In addition, under certain assumptions on the data, uniqueness of the solutions can be guaranteed and error estimates of the approximate solution are given. Moreover, some favourable properties of the discrete algebraic system are discussed.

76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations
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