Finite Element Simulation in Surface and Subsurface Hydrology

ContentsPreface Chapter 1 Introduction 1.1 Purpose and Scope of the Book 1.2 Approximations, Errors, and Significant Figures 1.3 Initial Value and Initial Boundary Value Problems 1.4 Classification of Partial Differential Equations 1.5 Matrix Operations Related to the Finite Element Method 1.6 Direct Methods for the Solution of Linear Algebraic Equations 1.7 Iterative Methods for the Solution of Linear Algebraic Equations References Chapter 2 Introduction to Finite Difference Theory 2.1 Why Consider Finite Difference Theory? 2.2 Finite Difference Approximations 2.3 Temporal Finite Difference Approximations References Chapter 3 The Method of Weighted Residuals 3.1 Finite Element Applications 3.2 The Fundamentals of Weighted Residual Procedures 3.3 Galerkin's Method 3.4 Convergence of the Finite Element Method 3.5 Approximations in the Time Domain 3.6 Summary of Approximation Methods References Chapter 4 Finite Elements 4.1 The Finite Element Concept 4.2 Linear Basis Functions 4.3 Higher-Degree Polynomial Basis Functions 4.4 Hermitian Polynomials 4.5 Transient Problem in One Space Variable 4.6 Finite Elements in Two Space Dimensions 4.7 Relationship between the Finite Element and Finite Difference Methods 4.8 Triangular Finite Elements in Two Space Dimensions 4.9 Use of Triangular Finite Elements in Two Space Dimensions for Transient Problems 4.10 Curved Isoparametric Elements 4.11 Three-Dimensional Elements 4.12 Odds and Ends References Chapter 5 Finite Element Method in Subsurface Hydrology 5.1 Introduction 5.2 Flow of Homogeneous Fluids in Saturated Porous Media 5.3 Flow of Nonhomogeneous Fluids in Saturated Porous Media 5.4 Saturated-Unsaturated Flows 5.5 Saturated-Unsaturated Flow of a Single Fluid 5.6 Saturated-Unsaturated Transport References Chapter 6 Lakes 6.1 Introduction 6.2 The Equations Which Describe the Flow 6.3 Simplified Flow Model 6.4 Generalized Flow Model 6.5 Hydrothermal Model for Lakes 6.6 Conclusions References Chapter 7 Analysis of Model Behavior 7.1 Stability and Consistency 7.2 Equations and Restrictions 7.3 Analytical Solution 7.4 Numerical Solution 7.5 Central Implicit Scheme on Linear Elements 7.6 Higher-Order Central Implicit Scheme 7.7 Alternative Time Stepping Scheme 7.8 Uncentered Implicit Scheme References Chapter 8 Estuaries and Coastal Regions 8.1 Scope of the Study 8.2 Basic Equations 8.3 Linearized Hydrodynamic Model 8.4 Implicit Nonlinear Model 8.5 Contaminant Transport in Estuaries 8.6 Summary References Index