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A new local stabilized nonconforming finite element method for the Stokes equations. (English) Zbl 1155.65101

The authors propose and study a new local stabilized nonconforming finite method based on two local Gauss integrations for the two-dimensional Stokes equation. The propose method uses the lowest equal-order pair of mixed finite elements. The authors prove the stability of this method and obtain optimal-order error estimates. In addition, they give numerical experiments to confirm the theoretical analysis, and compare then with some classical, closely related mixed finite element pairs. The results of this proposed method show its better performance than others.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35Q30 Navier-Stokes equations
65N15 Error bounds for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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References:

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