Stabilized nonconforming finite element methods for data assimilation in incompressible flows

A stabilized nonconforming finite element method for incompressible flow

In this paper we extend the recently introduced edge stabilization method to the case of nonconforming finite element approximations of the linearized Navier-Stokes equation. To get stability also in the convective dominated regime we add a term giving L2-control of the jump in the gradient over element boundaries. An a priori error estimate that is uniform in the Reynolds number is proved and ...

hTools for Predicting Incompressible Flows via Nonconforming Finite Element Models

Stabilized Finite Element Methods for the Velocity-Pressure-Stress Formulation of Incompressible Flows

Formulated in terms of velocity, pressure and the extra stress tensor, the incompressible Navier-Stokes equations are discretized by stabilized finite element methods. The stabilized methods proposed are analyzed for a linear model and extended to the Navier-Stokes equations. The numerical tests performed confirm the good stability characteristics of the methods. These methods are applicable to...

Least Squares Finite Element Methods for Viscous, Incompressible Flows

This paper is concerned with finite element methods of least-squares type for the approximate numerical solution of incompressible, viscous flow problems. Our main focus is on issues that are critical for the success of the finite element methods, such as decomposition of the Navier-Stokes equations into equivalent first-order systems, mathematical prerequisites for the optimality of the method...

Multigrid methods for stabilized nonconforming finite elements for incompressible flow involving the deformation tensor formulation

Edge-oriented stabilization methods in the framework of discontinuous Galerkin approaches have been recently proposed by Brenner [3] and particularly by Hansbo and Larson [5] for nonconforming finite element discretizations to satisfy a discrete Korn’s inequality. We develop and analyse corresponding multigrid components in combination with local Pressure-Schur-Complement methods and give numer...