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Zbl 1011.76041
Blasco, J.; Codina, R.
Space and time error estimates for a first-order, pressure-stabilized finite element method for the incompressible Navier-Stokes equations. (English)
[J] Appl. Numer. Math. 38, No.4, 475-497 (2001). ISSN 0168-9274

Summary: We analyze a pressure-stabilized finite element method for unsteady incompressible Navier-Stokes equations in primitive variables, for the time discretization we focus on a fully implicit monolithic scheme. We provide some error estimates for fully discrete solution which show that the velocity is first-order accurate in time step and attains optimal order accuracy in the mesh size for a given spatial interpolation, both in the spaces $L^2(\Omega)$ and $H^1_0(\Omega)$; the pressure solution is shown to be of order ${1\over 2}$ accurate in time step and also optimal in mesh size. These estimate are proved assuming only a weak compatibility condition on approximating spaces of velocity and pressure, which is satisfied by equal-order interpolations.

MSC 2000:: *76M10 Finite element methods
76D05 Navier-Stokes equations (fluid dynamics)
65M15 Error bounds (IVP of PDE)

Keywords: pressure-stabilized finite element method; unsteady incompressible Navier-Stokes equations; primitive variables; error estimates; velocity; time step; mesh size; pressure; weak compatibility condition; equal-order interpolations

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