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Space and time error estimates for a first-order, pressure-stabilized finite element method for the incompressible Navier-Stokes equations. (English) Zbl 1011.76041
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:
76M10Finite element methods (fluid mechanics)
76D05Navier-Stokes equations (fluid dynamics)
65M15Error bounds (IVP of PDE)
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References:
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