Finite Element Methods for Navier-Stokes Equations

1. Front Matter

   Pages i-x

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2. Mathematical Foundation of the Stokes Problem

   • Vivette Girault, Pierre-Arnaud Raviart

   Pages 1-111

3. Numerical Solution of the Stokes Problem in the Primitive Variables

   • Vivette Girault, Pierre-Arnaud Raviart

   Pages 112-192

4. Incompressible Mixed Finite Element Methods for Solving the Stokes Problem

   • Vivette Girault, Pierre-Arnaud Raviart

   Pages 193-277

5. Theory and Approximation of the Navier-Stokes Problem

   • Vivette Girault, Pierre-Arnaud Raviart

   Pages 278-367

6. Back Matter

   Pages 368-376

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The material covered by this book has been taught by one of the authors in a post-graduate course on Numerical Analysis at the University Pierre et Marie Curie of Paris. It is an extended version of a previous text (cf. Girault & Raviart [32J) published in 1979 by Springer-Verlag in its series: Lecture Notes in Mathematics. In the last decade, many engineers and mathematicians have concentrated their efforts on the finite element solution of the Navier-Stokes equations for incompressible flows. The purpose of this book is to provide a fairly comprehen­ sive treatment of the most recent developments in that field. To stay within reasonable bounds, we have restricted ourselves to the case of stationary prob­ lems although the time-dependent problems are of fundamental importance. This topic is currently evolving rapidly and we feel that it deserves to be covered by another specialized monograph. We have tried, to the best of our ability, to present a fairly exhaustive treatment of the finite element methods for inner flows. On the other hand however, we have entirely left out the subject of exterior problems which involve radically different techniques, both from a theoretical and from a practical point of view. Also, we have neither discussed the implemen­ tation of the finite element methods presented by this book, nor given any explicit numerical result. This field is extensively covered by Peyret & Taylor [64J and Thomasset [82].

• finite element method
• mathematics
• numerical analysis

• Laboratoire associé 189, Analyse Numérique, Université Pierre et Marie Curie, Paris VI, Paris Cedex 05, France

  Vivette Girault, Pierre-Arnaud Raviart

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