Dual-mixed finite element methods for the Navier-Stokes equations

Dual-mixed Finite Element Methods for the Navier-stokes Equations

A mixed finite element method for the Navier–Stokes equations is introduced in which the stress is a primary variable. The variational formulation retains the mathematical structure of the Navier–Stokes equations and the classical theory extends naturally to this setting. Finite element spaces satisfying the associated inf–sup conditions are developed. Mathematics Subject Classification. 65N60,...

Finite Element Methods for the Incompressible Navier-Stokes Equations

These notes are based on lectures given in a Short Course on Theoretical and Numerical Fluid Mechanics in Vancouver, British Columbia, Canada, July 27-28, 1996, and at several other places since then. They provide an introduction to recent developments in the numerical solution of the Navier-Stokes equations by the finite element method. The material is presented in eight sections:

Comparison of Finite Element Methods for the Navier-Stokes Equations

A Mixed Finite Element Method for Navier-stokes Equations

This paper describes a numerical solution of Navier-Stokes equations. It includes algorithms for discretization by finite element methods and a posteriori error estimation of the computed solutions. In order to evaluate the performance of the method, the numerical results are compared with some previously published works or with others coming from commercial code like ADINA system. AMS Mathemat...

Augmented Mixed Finite Element Methods for the Stationary Stokes Equations

Abstract. In this paper we introduce and analyze two augmented mixed finite element methods for a velocity-pressure-stress formulation of the stationary Stokes equations. Our approach, which extends analogue results for linear elasticity problems, is based on the introduction of the Galerkin least-squares type terms arising from the constitutive and equilibrium equations, and the Dirichlet boun...