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A stabilized finite element method for generalized stationary incompressible flows. (English) Zbl 0996.76045

The paper presents a stabilized finite element approach for numerical solution of incompressible Navier-Stokes equations including Coriolis force and permeability terms. The method is based on an algebraic version of sub-grid scale approach. A mathematically rigorous analysis of stability and convergence of the method is given, from which the author also derives expressions for two algorithmic parameters involved in the scheme. Optimal error estimates are achieved with these parameters. Numerical results for several test cases with different Coriolis force and permeability parameters confirm the theoretical results. Comparisons with results obtained with standard Galerkin approach show the superiority of the stabilized scheme.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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