Incompressible Flow and the Finite Element Method, Volume 1: Advection-Diffusion and Isothermal Laminar Flow

Preface
Glossary of Abbreviations
1. Introduction
1.1 Introduction
1.2 Incompressible Flow
1.3 The Finite Element Method
1.4 Incompressible Flow and the Finite Element Method
1.5 Overview of this Volume
1.6 Some Subjective Discussion
1.7 Why Finite Elements? Why Not Finite Volumes?
2. The Advection-Diffusion Equation
2.1 The Continuum Equation
2.2 The Finite Element Equations /
Discretization of the Weak Form
2.3 Some Semi-Discrete Equations
2.4 Open Boundary Conditions (OBC's)
2.5 Some Non-Galerkin Results
2.6 Dispersion, Dissipation, Phase Speed, Group Velocity, Mesh Design, and Wiggles
2.7 Time Integration
2.8 Additional Numerical Examples
Appendix 1 Some Element Matrices
A.1.1 Advection Diffusion Matrices
A.1.2 One-Dimensional Element Matrices
A.1.3 Two-Dimensional Element Matrices
A.1.4 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 Scalar Projections, Orthogonal and Not and
Projection Methods
A.3.1 Introduction
A.3.2 Scalar Projections
References
Author Index
Subject Index