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A fully discrete stabilized finite element method for the time-dependent Navier-Stokes equations. (English) Zbl 1172.76027
Summary: We consider a fully discrete stabilized finite element method based on two local Gauss integrations for two-dimensional time-dependent Navier-Stokes equations. It focuses on the lowest equal-order velocity-pressure pairs. Unlike the other stabilized method, the present approach does not require specification of a stabilization parameter or calculation of higher-order derivatives, and always leads to a symmetric linear system. The Euler semi-implicit scheme is used for the time discretization. It is shown that the proposed fully discrete stabilized finite element method results in the optimal order bounds for velocity and pressure.

76M10Finite element methods (fluid mechanics)
76D05Navier-Stokes equations (fluid dynamics)
76M20Finite difference methods (fluid mechanics)
65M15Error bounds (IVP of PDE)
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
Full Text: DOI
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