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Space and time error estimates for a first order, pressure stabilized finite element method for the incompressible Navier-Stokes equations
Blasco Lorente, Jorge; Codina, Ramon
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
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.
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
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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