Incompressible Flow and the Finite Element Method, 2 Volume Set

1. Glossary of Abbreviations

2. Preface and Introduction

3. The Navier-Stokes Equations

Notational Introduction

The Continuum Equations

Alternate Forms of the Viscous Term

Alternate Forms of the Non-Linear Term

Derived Equations

Alternate Statements of the NS Equations

Special Cases of Interest

Boundary Conditions

Initial Conditions (and Well-Posedness)

Interim Summary

Global Conservation Laws

Weak Form of the PDEhod

Variational Principles for Potential and Stokes Flow

Solution Methods for the Semi_Discretized Time-Dependent (and Steady) Equations

Aliasing and Aliasing Instability, Linear and Non-Linear

A New Look at Two Old Finite Difference Methods

Numerical Example

Closure: Some Additional Remarks on the Pressure

4. Derived Quantities

Introduction

Two Dimensions

Three Dimensions

Appendix 1 Some Element Matrix

Appendix 2 Further Comparison of Finite Elements and Finite Volumes

Appendix 3 Projections, Orthagonal and Not and Projection Methods

References

Author Index

Subject Index