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A refined mixed finite-element method for the stationary Navier-Stokes equations with mixed boundary conditions. (English) Zbl 1166.76028

Summary: This paper is concerned with the mixed formulation of Navier-Stokes equations with mixed boundary conditions in 2D polygonal domains and its numerical approximation. We first describe the regularity of any solution. The problem is then approximated by a mixed finite element method where the strain tensor and the antisymmetric gradient tensor, quantities of practical importance, are introduced as new unknowns. An existence result for the finite element solution and convergence results are proved near a nonsingular solution. Quasi-optimal error estimates are finally presented.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
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