Numerische Mathematik

, Volume 87, Issue 1, pp 59–81

Analysis of a pressure-stabilized finite element approximation of the stationary Navier-Stokes equations

  • Ramon Codina
  • Jordi Blasco
Original article

DOI: 10.1007/s002110000174

Cite this article as:
Codina, R. & Blasco, J. Numer. Math. (2000) 87: 59. doi:10.1007/s002110000174

Summary.

The purpose of this paper is to analyze a finite element approximation of the stationary Navier-Stokes equations that allows the use of equal velocity-pressure interpolation. The idea is to introduce as unknown of the discrete problem the projection of the pressure gradient (multiplied by suitable algorithmic parameters) onto the space of continuous vector fields. The difference between these two vectors (pressure gradient and projection) is introduced in the continuity equation. The resulting formulation is shown to be stable and optimally convergent, both in a norm associated to the problem and in the \(L^2\) norm for both velocities and pressure. This is proved first for the Stokes problem, and then it is extended to the nonlinear case. All the analysis relies on an inf-sup condition that is much weaker than for the standard Galerkin approximation, in spite of the fact that the present method is only a minor modification of this.

Mathematics Subject Classification (1991): 65N30, 76D05

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Ramon Codina
    • 1
  • Jordi Blasco
    • 2
  1. 1.Universitat Politècnica de Catalunya, Jordi Girona 1–3, Edifici C1, 08034 Barcelona, Spain; e-mail: ramon.codina@upc.esES
  2. 2.e-mail: blasco@mA1.upc.esES