This paper develops and analyzes two least-squares methods for the numerical solution of linear, stationary incompressible Newtonian fluid flow in two and three dimensions. Both approaches use the L norm to define least-squares functionals. One is based on the stress-velocity formulation (see section 3.2), and it applies to general boundary conditions. The other is based on an equivalent formul...

In this paper, we develop least-squares finite element methods (LSFEMs) for incompressible fluid flows with improved mass conservation. Specifically, we formulate a new locally conservative LSFEM for the velocity– vorticity–pressure Stokes system, which uses a piecewise divergence-free basis for the velocity and standard C 0 elements for the vorticity and the pressure. The new method, which we ...

We propose and analyse an augmented mixed finite element method for the Oseen equations written in terms of velocity, vorticity, pressure with non-constant viscosity homogeneous Dirichlet boundary condition velocity. The weak formulation includes least-squares arising from constitutive equation incompressibility condition, we show that it satisfies hypotheses Babu\vska-Brezzi theory. Repeating ...

Shallow-water equations discretized on a perfect hexagonal grid are analyzed using both a momentum formulation and a vorticity-divergence formulation. The vorticity-divergence formulation uses the unstaggered Z grid that places mass, vorticity, and divergence at the centers of the hexagons. The momentum formulation uses the staggered ZM grid that places mass at the centers of the hexagons and v...

The pseudostress-velocity formulation of the stationary Stokes problem allows a Raviart-Thomas mixed finite element formulation with quasi-optimal convergence and some superconvergent reconstruction of the velocity. This local postprocessing gives rise to some averaging a posteriori error estimator with explicit constants for reliable error control. Standard residual-based explicit a posteriori...

We consider the Stokes problem provided with non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We write a variational formulation of this problem with three independent unknowns: the vorticity, the velocity and the pressure. Next we propose a discretization by spectral element methods which relies on this formulat...

We present preliminary results of a high order WENO scheme applied to deterministic computations for two dimensional formulation of the transients for the Boltzmann-Poisson system describing electron transport in semiconductor devices. The collisional form models optical-phonon interactions which become dominant under strong energetic conditions corresponding to nanoscale active regions under a...

The influence of the location of the lateral boundaries on 2D computation of unsteady incompressible flow past a circular cylinder is investigated. The case of Reynolds number 100 is used as a benchmark, and several quantities characterizing the unsteady flow are obtained for a range of lateral boundary locations. The computations are performed with two distinct finite element formulations – sp...

Finite element procedures and computations based on the velocity-pressure and vorticitystream function formulations of incompressible flows are presented. Two new multi-step velocity-pressure formulations are proposed and are compared with the vorticity-stream function and one-step formulations. The example problems chosen are the standing vortex problem and flow past a circular cylinder. Bench...