Analysis of a stabilized finite element approximation of the Oseen equations using orthogonal subscales

Authors:
Ramon Codina
Affiliations:
Universitat Politècnica de Catalunya, Jordi Girona 1-3, Edifici C1, 08034 Barcelona, Spain
Venue:
Applied Numerical Mathematics
Year:
2008

Citing 8
Cited 6

A new finite element formulation for computational fluid dynamics: V. Circumventing the Babusˇka-Brezzi condition: A stable Petrov-Galerkin formulation of

Computer Methods in Applied Mechanics and Engineering
Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations

Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
Mixed and hybrid finite element methods

Mixed and hybrid finite element methods
Error analysis of some Galerkin least squares methods for the elasticity equations

SIAM Journal on Numerical Analysis
Stabilized finite element methods. II: The incompressible Navier-Stokes equations

Computer Methods in Applied Mechanics and Engineering
Analysis of a streamline diffusion finite element method for the Stokes and Navier-Stokes equations

SIAM Journal on Numerical Analysis
Analysis of Velocity-Flux First-Order System Least-Squares Principles for the Navier--Stokes Equations: Part I

SIAM Journal on Numerical Analysis
Space and time error estimates for a first order, pressure stabilized finite element method for the incompressible Navier-Stokes equations

Applied Numerical Mathematics

Local projection stabilization for advection--diffusion--reaction problems: One-level vs. two-level approach

Applied Numerical Mathematics
Approximation of the thermally coupled MHD problem using a stabilized finite element method

Journal of Computational Physics
Long-Term Stability Estimates and Existence of a Global Attractor in a Finite Element Approximation of the Navier-Stokes Equations with Numerical Subgrid Scale Modeling

SIAM Journal on Numerical Analysis
Stokes, Maxwell and Darcy: A single finite element approximation for three model problems

Applied Numerical Mathematics
A Nodal-based Finite Element Approximation of the Maxwell Problem Suitable for Singular Solutions

SIAM Journal on Numerical Analysis
On an unconditionally convergent stabilized finite element approximation of resistive magnetohydrodynamics

Journal of Computational Physics

Quantified Score

Hi-index	0.01

Visualization

Abstract

In this paper we present a stabilized finite element formulation to solve the Oseen equations as a model problem involving both convection effects and the incompressibility restriction. The need for stabilization techniques to solve this problem arises because of the restriction in the possible choices for the velocity and pressure spaces dictated by the inf-sup condition, as well as the instabilities encountered when convection is dominant. Both can be overcome by resorting from the standard Galerkin method to a stabilized formulation. The one presented here is based on the subgrid scale concept, in which unresolvable scales of the continuous solution are approximately accounted for. In particular, the approach developed herein is based on the assumption that unresolved subscales are orthogonal to the finite element space. It is shown that this formulation is stable and optimally convergent for an adequate choice of the algorithmic parameters on which the method depends.