Model of approximation of a velocity, vorticity and pressure in an incompressible fluid

Abstract

Generally, the temporary discretization of the Navier-Stokes equations despise the convective term, and consider a boundary ∂Ω = . This paper introduces a Galerkin scheme designed to solve by means of the finite element method for the Oseen problem in three dimensions written in terms of speed, vorticity and pressure, in a viscous and incompressible fluid that flows through a porous medium, this problem is obtained from a temporary discretization of the Navier-Stokes equations and we consider a partitioned boundary ∂Ω = Γ1 ∪ Γ2 and disjoint, that is, the velocity is of the homogeneous Dirichlet type on Γ1, while the tangential velocity and pressure They are of the non-homogeneous Dirichlet type on Γ2. In the variational formulation the speed is completely decoupled, which allows you to approximate the vorticity and pressure independently. The speed is recovered from the vorticity and pressure. Galerkin’s scheme is based on Nédélec finite elements and continuous polynomials to pieces of the same order, for vorticity and pressure, respectively. Likewise, convergence rates are obtained for vorticity, speed and pressure in natural norms. Finally, a numerical example is provided that illustrates the behavior of the model.