Numerical Solution of the Stokes Problem in the Primitive Variables

  • Vivette Girault
  • Pierre-Arnaud Raviart
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 5)

Abstract

The abstract problem discussed in Chapter I, § 4 lends itself readily to a straight-forward approximation that converges under reasonable assumptions with an error proportional to the approximation error of the spaces involved. When applied to the Stokes problem, this approach yields a conforming approximation of the velocity and pressure, although the approximate velocity field is (in general) not exactly divergence-free. The wide range of finite element methods developped in the remainder of the chapter are all founded on the material of this paragraph. Non-conforming methods can also be put into this framework (cf. Zine [85]) but for the sake of conciseness we have skipped them entirely.

Keywords

Finite Element Method Bilinear Form Affine Transformation Stokes Problem Continuous Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Vivette Girault
    • 1
  • Pierre-Arnaud Raviart
    • 1
  1. 1.Laboratoire associé 189, Analyse NumériqueUniversité Pierre et Marie Curie, Paris VIParis Cedex 05France

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