Incompressible Flow and the Finite Element Method

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