Galerkin Finite Element Methods with Symmetric Pressure Stabilization for the Transient Stokes Equations: Stability and Convergence Analysis

Galerkin Finite Element Methods with Symmetric Pressure Stabilization for the Transient Stokes Equations: Stability and Convergence Analysis

We consider the stability and convergence analysis of pressure stabilized finite element approximations of the transient Stokes’ equation. The analysis is valid for a class of symmetric pressure stabilization operators, but also for standard, inf-sup stable, velocity/pressure spaces without stabilization. Provided the initial data is chosen as a specific (method dependent) Ritz-projection, we g...

Finite Element Methods for Stokes Equations

1. STOKES EQUATIONS In this section, we shall study the well posedness of the weak formulation of the steadystate Stokes equations −μ∆u +∇p = f , (1) −divu = 0, (2) where u can be interpreted as the velocity field of an incompressible fluid motion, and p is then the associated pressure, the constant μ is the viscosity coefficient of the fluid. For simplicity, we consider homogenous Dirichlet bo...

Discontinuous Galerkin Finite Element Methods for the Navier–Stokes Equations in Entropy Variable Formulation

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