Finite Element Methods for Incompressible Flow Problems

1. Front Matter

   Pages i-xiii

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2. Introduction

   • Volker John

   Pages 1-6

3. The Navier–Stokes Equations as Model for Incompressible Flows

   • Volker John

   Pages 7-24

4. Finite Element Spaces for Linear Saddle Point Problems

   • Volker John

   Pages 25-135

5. The Stokes Equations

   • Volker John

   Pages 137-242

6. The Oseen Equations

   • Volker John

   Pages 243-300

7. The Steady-State Navier–Stokes Equations

   • Volker John

   Pages 301-353

8. The Time-Dependent Navier–Stokes Equations: Laminar Flows

   • Volker John

   Pages 355-445

9. The Time-Dependent Navier–Stokes Equations: Turbulent Flows

   • Volker John

   Pages 447-647

10. Solvers for the Coupled Linear Systems of Equations

    • Volker John

    Pages 649-675

11. Back Matter

    Pages 677-812

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This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.

• Stokes and Navier-Stokes equations
• finite element analysis
• saddle point problems
• turbulence problems
• support of analysis by numerical results
• partial differential equations

“Important distinction of this book is its extensive and detailed treatment of many turbulence models, subgrid models, and stabilization methods. … this is a very well written encyclopedic book, which I strongly recommend to anybody interested in finite element methods and incompressible fluids.” (Maxim A. Olshanskii, SIAM Review, Vol. 60 (1), 2018)

• Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

  Volker John

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