A Finite Spectral Finite Element Method for Incompressible Navier-Stokes Equations

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:

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...

A multiscale finite element method for the incompressible Navier–Stokes equations

This paper presents a new multiscale finite element method for the incompressible Navier–Stokes equations. The proposed method arises from a decomposition of the velocity field into coarse/resolved scales and fine/unresolved scales. Modeling of the unresolved scales corrects the lack of stability of the standard Galerkin formulation and yields a method that possesses superior properties like th...

A Characteristics-Mix Stabilized Finite Element Method for Variable Density Incompressible Navier-Stokes Equations

This paper describes a characteristics-mix finite element method for the computation of incompressible Navier-Stokes equations with variable density. We have introduced a mixed scheme which combines a characteristics finite element scheme for treating the mass conservation equation and a finite element method to deal with the momentum equation and the divergence free constraint. The proposed me...

An Adaptive Finite Element Method for the Incompressible Navier{stokes Equations on Time-dependent Domains