Space and time error estimates for a first order, pressure stabilized finite element method for the incompressible Navier-Stokes equations
In this paper we analyse 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 sh...
| Autores: | , |
|---|---|
| Tipo de documento: | artigo |
| Data de publicação: | 1999 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/770 |
| Acesso em linha: | https://hdl.handle.net/2117/770 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Fluid mechanics Partial differential equations Finite elements Incompressible flow Pressure instability Navier-Stokes equations Fluids Vorticitat -- Teoria Mecànica de fluids Equacions en derivades parcials Problemes de valor inicial Problemes de contorn Classificació AMS::65 Numerical analysis::65M Partial differential equations, initial value and time-dependent initial-boundary value problems Classificació AMS::76 Fluid mechanics::76D Incompressible viscous fluids Classificació AMS::76 Fluid mechanics::76M Basic methods in fluid mechanics |
| Resumo: | In this paper we analyse 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 L^2(W) and H(W) the pressure solution is shown to be order 1/2 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. |
|---|