{"product_id":"practical-finite-element-modeling-in-earth-science-using-matlab-9781119248620","title":"Practical Finite Element Modeling in Earth","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eMathematical models have become a crucial way for the Earth scientist to understand and predict how our planet functions and evolves through time and space. The finite element method (FEM) is a remarkably flexible and powerful tool with enormous potential in the Earth Sciences.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xiii\u003c\/p\u003e \u003cp\u003eSymbols xv\u003c\/p\u003e \u003cp\u003eAbout the Companion Website xvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I The Finite Element Method with Matlab 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Preliminaries 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Mathematical Models 3\u003c\/p\u003e \u003cp\u003e1.2 Boundary and Initial Conditions 4\u003c\/p\u003e \u003cp\u003e1.3 Analytical Solutions 5\u003c\/p\u003e \u003cp\u003e1.4 Numerical Solutions 5\u003c\/p\u003e \u003cp\u003e1.5 Numerical Solution Methods 7\u003c\/p\u003e \u003cp\u003e1.6 Matlab Script 8\u003c\/p\u003e \u003cp\u003e1.7 Exercises 10\u003c\/p\u003e \u003cp\u003eSuggested Reading 12\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Beginning with the Finite Element Method 13\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 The Governing PDE 13\u003c\/p\u003e \u003cp\u003e2.2 Approximating the Continuous Variable 14\u003c\/p\u003e \u003cp\u003e2.3 Minimizing the Residual 15\u003c\/p\u003e \u003cp\u003e2.4 Evaluating the Element Matrices 17\u003c\/p\u003e \u003cp\u003e2.5 Time Discretization 18\u003c\/p\u003e \u003cp\u003e2.6 Assembly 19\u003c\/p\u003e \u003cp\u003e2.7 Boundary and Initial Conditions 21\u003c\/p\u003e \u003cp\u003e2.8 Solution of the Algebraic Equations 21\u003c\/p\u003e \u003cp\u003e2.9 Exercises 22\u003c\/p\u003e \u003cp\u003eSuggested Reading 23\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Programming the Finite Element Method in Matlab 25\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Program Structure and Philosophy 25\u003c\/p\u003e \u003cp\u003e3.2 Summary of the Problem 25\u003c\/p\u003e \u003cp\u003e3.3 Discretized Equations 26\u003c\/p\u003e \u003cp\u003e3.4 The Program 27\u003c\/p\u003e \u003cp\u003e3.4.1 Preprocessor Stage 27\u003c\/p\u003e \u003cp\u003e3.4.2 Solution Stage 29\u003c\/p\u003e \u003cp\u003e3.4.3 Postprocessor Stage 30\u003c\/p\u003e \u003cp\u003e3.5 Matlab Script 30\u003c\/p\u003e \u003cp\u003e3.6 Exercises 33\u003c\/p\u003e \u003cp\u003eSuggested Reading 34\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Numerical Integration and Local Coordinates 35\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Gauss–Legendre Quadrature 36\u003c\/p\u003e \u003cp\u003e4.2 Local Coordinates 37\u003c\/p\u003e \u003cp\u003e4.3 Evaluating the Integrals 39\u003c\/p\u003e \u003cp\u003e4.4 Variable Material Properties 40\u003c\/p\u003e \u003cp\u003e4.5 Programming Considerations 41\u003c\/p\u003e \u003cp\u003e4.6 Matlab Script 43\u003c\/p\u003e \u003cp\u003e4.7 Exercises 45\u003c\/p\u003e \u003cp\u003eSuggested Reading 47\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 The Finite Element Method in Two Dimensions 49\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Discretization 50\u003c\/p\u003e \u003cp\u003e5.2 Geometry and Nodal Connectivity 52\u003c\/p\u003e \u003cp\u003e5.3 Integration of Element Matrices 54\u003c\/p\u003e \u003cp\u003e5.4 Multielement Assembly 57\u003c\/p\u003e \u003cp\u003e5.5 Boundary Conditions and Solution 60\u003c\/p\u003e \u003cp\u003e5.6 Matlab Script 61\u003c\/p\u003e \u003cp\u003e5.7 Exercises 65\u003c\/p\u003e \u003cp\u003eSuggested Reading 66\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 The Finite Element Method in Three Dimensions 67\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Discretization 67\u003c\/p\u003e \u003cp\u003e6.2 Element Integration 69\u003c\/p\u003e \u003cp\u003e6.3 Assembly for Multielement Mesh 72\u003c\/p\u003e \u003cp\u003e6.4 Boundary Conditions and Solution 73\u003c\/p\u003e \u003cp\u003e6.5 Matlab Program 74\u003c\/p\u003e \u003cp\u003e6.6 Exercises 79\u003c\/p\u003e \u003cp\u003eSuggested Reading 80\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Generalization of Finite Element Concepts 81\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 The FEM for an Elliptic Problem 84\u003c\/p\u003e \u003cp\u003e7.2 The FEM for a Hyperbolic Problem 96\u003c\/p\u003e \u003cp\u003e7.3 The FEM for Systems of Equations 102\u003c\/p\u003e \u003cp\u003e7.4 Exercises 116\u003c\/p\u003e \u003cp\u003eSuggested Reading 116\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Applications of the Finite Element Method in Earth Science 119\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Heat Transfer 121\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Conductive Cooling in an Eroding Crust 122\u003c\/p\u003e \u003cp\u003e8.2 Conductive Cooling of an Intrusion 126\u003c\/p\u003e \u003cp\u003eSuggested Reading 135\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Landscape Evolution 137\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Evolution of a 1D River Profile 138\u003c\/p\u003e \u003cp\u003e9.2 Evolution of a Fluvially Dissected Landscape 143\u003c\/p\u003e \u003cp\u003eSuggested Reading 150\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Fluid Flow in Porous Media 151\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Fluid Flow Around a Fault 152\u003c\/p\u003e \u003cp\u003e10.2 Viscous Fingering 157\u003c\/p\u003e \u003cp\u003eSuggested Reading 166\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Lithospheric Flexure 167\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Governing Equations 167\u003c\/p\u003e \u003cp\u003e11.2 FEM Discretization 168\u003c\/p\u003e \u003cp\u003e11.3 Matlab Implementation 171\u003c\/p\u003e \u003cp\u003eSuggested Reading 181\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Deformation of Earth’s Crust 183\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Governing Equations 183\u003c\/p\u003e \u003cp\u003e12.2 Rate Formulation 185\u003c\/p\u003e \u003cp\u003e12.3 FEM Discretization 186\u003c\/p\u003e \u003cp\u003e12.4 Viscoelastoplasticity 188\u003c\/p\u003e \u003cp\u003e12.5 Matlab Implementation 190\u003c\/p\u003e \u003cp\u003eSuggested Reading 205\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Going Further 207\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Optimization 207\u003c\/p\u003e \u003cp\u003e13.2 Using Other FEMs 213\u003c\/p\u003e \u003cp\u003e13.3 Use of Existing Finite Element Software 215\u003c\/p\u003e \u003cp\u003eAppendix A Derivation of the Diffusion Equation 217\u003c\/p\u003e \u003cp\u003eAppendix B Basics of Linear Algebra with Matlab 221\u003c\/p\u003e \u003cp\u003eAppendix C Comparison between Different Numerical Methods 227\u003c\/p\u003e \u003cp\u003eAppendix D Integration by Parts 237\u003c\/p\u003e \u003cp\u003eAppendix E Time Discretization 239\u003c\/p\u003e \u003cp\u003eReferences 241\u003c\/p\u003e \u003cp\u003eIndex 245\u003c\/p\u003e","brand":"John Wiley and Sons Ltd","offers":[{"title":"Default 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