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| − | In this paper we analyze a pressure stabilized, finite element method for the 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 the fully discrete solution which show that the velocity is first order accurate in the time step and attains optimal order accuracy in the mesh size for the given spatial interpolation, both in the spaces <math>L^2(\ | + | In this paper we analyze a pressure stabilized, finite element method for the 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 the fully discrete solution which show that the velocity is first order accurate in the time step and attains optimal order accuracy in the mesh size for the given spatial interpolation, both in the spaces <math>L^2(\Omega)</math> and <math>(H^1)_0(\Omega)</math>; the pressure solution is shown to be order 12 accurate in the time step and also optimal in the mesh size. These estimates are proved assuming only a weak compatibility condition on the approximating spaces of velocity and pressure, which is satisfied by equal order interpolations. |
<pdf>Media:Draft_Samper_167050818_4650_1-s2.0-S0168927401000484-main.pdf</pdf> | <pdf>Media:Draft_Samper_167050818_4650_1-s2.0-S0168927401000484-main.pdf</pdf> | ||
Revision as of 14:21, 2 September 2019
Abstract
In this paper we analyze a pressure stabilized, finite element method for the 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 the fully discrete solution which show that the velocity is first order accurate in the time step and attains optimal order accuracy in the mesh size for the given spatial interpolation, both in the spaces and ; the pressure solution is shown to be order 12 accurate in the time step and also optimal in the mesh size. These estimates are proved assuming only a weak compatibility condition on the approximating spaces of velocity and pressure, which is satisfied by equal order interpolations.
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Published on 01/01/2001
DOI: 10.1016/S0168-9274(01)00048-4
Licence: CC BY-NC-SA license
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