Incompressible Flow and the Finite Element Method, Volume 2

Glossary of Abbreviations
Preface and Introduction
3. The Navier-Stokes Equations
3.1 Notational Introduction
3.2 The Continuum Equations
3.3 Alternate Forms of the Viscous Term
3.4 Alternate Forms of the Non-Linear Term
3.5 Derived Equations
3.6 Alternate Statements of the NS Equations
3.7 Special Cases of Interest
3.8 Boundary Conditions
3.9 Initial Conditions (and Well-Posedness)
3.10 Interim Summary
3.11 Global Conservation Laws
3.12 Weak Form of the PDE's /
Natural Boundary Conditions (NBC's)
3.13 The Finite Element Equations /
Discretization of the Weak Form
3.14 A Control Volume Finite Element Method
3.15 Variational Principles for Potential and Stokes Flow
3.16 Solution Methods for the Semi_Discretized Time-Dependent (and Steady) Equations
3.17 Aliasing and Aliasing Instability, Linear and Non-Linear
3.18 A New Look at Two Old Finite Difference Methods
3.19 Numerical Example -
Implusive Start
3.20 Closure: Some Additional Remarks on the Pressure
4. Derived Quantities
4.1 Introduction
4.2 Two Dimensions
4.3 Three Dimensions
Appendix 1 Some Element Matrix
A.1.1 Advection Diffusion Matrices
A.1.2 One-Dimensional Element Matrices
A.1.3 Two-Dimensional Element Matrices
A.1.4 Navier-Stokes: Additional Matrices
A.1.5 Two-Dimensional Control Volume Finite Element Matrices
Appendix 2 Further Comparison of Finite Elements and Finite
Volumes
A.2.1 Introduction
A.2.2 Viewpoint One
A.2.3 Viewpoint Two
Appendix 3 Projections, Orthagonal and Not and Projection Methods
A.3.1 Introduction
A.3.2 Scalar Projections
A.3.3 Vector Projections
References
Author Index
Subject Index