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A nonconforming finite element method for the stationary Navier-Stokes equations. (English) Zbl 0933.76047
The techniques carried out by the authors improve upon and extend those which they had previously introduced for the simpler case of the Stokes equations [the authors and G. A. Baker, SIAM J. Numer. Anal. 27, No. 6, 1466-1485 (1990; Zbl 0719.76047)]. In the present paper devoted to the Navier-Stokes equations, the velocity field is approximated using piecewise solenoidal functions which are discontinuous across the interelement boundary and which are pointwise divergence-free on each element. The pressure is approximated by continuous functions. Eventually, optimal rates of convergence are obtained. The only price is a local quasi-uniformity requirement imposed on the meshes.

76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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