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Two-level Brezzi-Pitkäranta stabilized finite element methods for the incompressible flows. (English) Zbl 1474.76036

Summary: We present a new stabilized finite element method for incompressible flows based on Brezzi-Pitkäranta stabilized method. The stability and error estimates of finite element solutions are derived for classical one-level method. Combining the techniques of two-level discretizations, we propose two-level Stokes/Oseen/Newton iteration methods corresponding to three different linearization methods and show the stability and error estimates of these three methods. We also propose a new Newton correction scheme based on the above two-level iteration methods. Finally, some numerical experiments are given to support the theoretical results and to check the efficiency of these two-level iteration methods.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35Q30 Navier-Stokes equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
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