{"product_id":"an-introduction-to-the-finite-element-method-for-differential-equations-hardback-9781119671640","title":"An Introduction to the Finite Element Method for Differential Equations (Hardback) 9781119671640","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eAn Introduction to the Finite Element Method for Differential Equations\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eMohammad Asadzadeh (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781119671640, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 26 October 2020\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e352 pages\u003cbr\u003e22.9 x 15.5 x 2 cm, 0.68 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003cb\u003eMaster the finite element method with this masterful and practical volume\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eAn Introduction to the Finite Element Method (FEM) for Differential Equations\u003c\/i\u003e provides readers with a practical and approachable examination of the use of the finite element method in mathematics. Author Mohammad Asadzadeh covers basic FEM theory, both in one-dimensional and higher dimensional cases.\u003c\/p\u003e \u003cp\u003eThe book is filled with concrete strategies and useful methods to simplify its complex mathematical contents. Practically written and carefully detailed, \u003ci\u003eAn Introduction to the Finite Element Method\u003c\/i\u003e covers topics including:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eAn introduction to basic ordinary and partial differential equations\u003c\/li\u003e \u003cli\u003eThe concept of fundamental solutions using Green's function approaches\u003c\/li\u003e \u003cli\u003ePolynomial approximations and interpolations, quadrature rules, and iterative numerical methods to solve linear systems of equations\u003c\/li\u003e \u003cli\u003eHigher-dimensional interpolation procedures\u003c\/li\u003e \u003cli\u003eStability and convergence analysis of FEM for differential equations\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThis book is ideal for upper-level undergraduate and graduate students in natural science and engineering. It belongs on the shelf of anyone seeking to improve their understanding of differential equations.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003ePreface \u003ci\u003exi\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003eAcknowledgments \u003ci\u003exiii\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction \u003c\/b\u003e\u003cb\u003e1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Preliminaries 2\u003c\/p\u003e \u003cp\u003e1.2 Trinities for Second-Order PDEs 4\u003c\/p\u003e \u003cp\u003e1.3 PDEs in ℝ\u003ci\u003en\u003c\/i\u003e, Further Classifications 10\u003c\/p\u003e \u003cp\u003e1.4 Differential Operators, Superposition 12\u003c\/p\u003e \u003cp\u003e1.4.1 Exercises 14\u003c\/p\u003e \u003cp\u003e1.5 Some Equations of Mathematical Physics 15\u003c\/p\u003e \u003cp\u003e1.5.1 The Poisson Equation 16\u003c\/p\u003e \u003cp\u003e1.5.2 The Heat Equation 17\u003c\/p\u003e \u003cp\u003e1.5.2.1 A Model Problem for the Stationary Heat Equation in 1\u003ci\u003ed \u003c\/i\u003e17\u003c\/p\u003e \u003cp\u003e1.5.2.2 Fourier’s Law of Heat Conduction, Derivation of the Heat Equation 18\u003c\/p\u003e \u003cp\u003e1.5.3 The Wave Equation 21\u003c\/p\u003e \u003cp\u003e1.5.3.1 The Vibrating String, Derivation of the Wave Equation in 1\u003ci\u003ed \u003c\/i\u003e21\u003c\/p\u003e \u003cp\u003e1.5.4 Exercises 24\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Mathematical Tools \u003c\/b\u003e\u003cb\u003e27\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Vector Spaces 27\u003c\/p\u003e \u003cp\u003e2.1.1 Linear Independence, Basis, and Dimension 30\u003c\/p\u003e \u003cp\u003e2.2 Function Spaces 33\u003c\/p\u003e \u003cp\u003e2.2.1 Spaces of Differentiable Functions 33\u003c\/p\u003e \u003cp\u003e2.2.2 Spaces of Integrable Functions 34\u003c\/p\u003e \u003cp\u003e2.2.3 Weak Derivative 35\u003c\/p\u003e \u003cp\u003e2.2.4 Sobolev Spaces 36\u003c\/p\u003e \u003cp\u003e2.2.5 Hilbert Spaces 37\u003c\/p\u003e \u003cp\u003e2.3 Some Basic Inequalities 38\u003c\/p\u003e \u003cp\u003e2.4 Fundamental Solution of PDEs 41\u003c\/p\u003e \u003cp\u003e2.4.1 Green’s Functions 43\u003c\/p\u003e \u003cp\u003e2.5 The Weak\/Variational Formulation 44\u003c\/p\u003e \u003cp\u003e2.6 A Framework for Analytic Solution in 1\u003ci\u003ed \u003c\/i\u003e46\u003c\/p\u003e \u003cp\u003e2.6.1 The Variational Formulation in 1\u003ci\u003ed \u003c\/i\u003e48\u003c\/p\u003e \u003cp\u003e2.6.2 The Minimization Problem in 1\u003ci\u003ed \u003c\/i\u003e51\u003c\/p\u003e \u003cp\u003e2.6.3 A Mixed Boundary Value Problem in 1\u003ci\u003ed \u003c\/i\u003e52\u003c\/p\u003e \u003cp\u003e2.7 An Abstract Framework 54\u003c\/p\u003e \u003cp\u003e2.7.1 Riesz and Lax–Milgram Theorems 57\u003c\/p\u003e \u003cp\u003e2.8 Exercises 63\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Polynomial Approximation\/Interpolation in 1\u003ci\u003ed \u003c\/i\u003e\u003c\/b\u003e\u003cb\u003e67\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Finite Dimensional Space of Functions on an Interval 67\u003c\/p\u003e \u003cp\u003e3.2 An Ordinary Differential Equation (ODE) 71\u003c\/p\u003e \u003cp\u003e3.2.1 Forward Euler Method to Solve IVP 71\u003c\/p\u003e \u003cp\u003e3.2.2 Variational Formulation for IVP 72\u003c\/p\u003e \u003cp\u003e3.2.3 Galerkin Method for IVP 73\u003c\/p\u003e \u003cp\u003e3.3 A Galerkin Method for (BVP) 74\u003c\/p\u003e \u003cp\u003e3.3.1 An Equivalent Finite Difference Approach 79\u003c\/p\u003e \u003cp\u003e3.4 Exercises 82\u003c\/p\u003e \u003cp\u003e3.5 Polynomial Interpolation in 1\u003ci\u003ed \u003c\/i\u003e83\u003c\/p\u003e \u003cp\u003e3.5.1 Lagrange Interpolation 90\u003c\/p\u003e \u003cp\u003e3.6 Orthogonal- and \u003ci\u003eL\u003c\/i\u003e2-Projection 94\u003c\/p\u003e \u003cp\u003e3.6.1 The \u003ci\u003eL\u003c\/i\u003e2-Projection onto the Space of Polynomials 94\u003c\/p\u003e \u003cp\u003e3.7 Numerical Integration, Quadrature Rule 96\u003c\/p\u003e \u003cp\u003e3.7.1 Composite Rules for Uniform Partitions 98\u003c\/p\u003e \u003cp\u003e3.7.2 Gauss Quadrature Rule 101\u003c\/p\u003e \u003cp\u003e3.8 Exercises 105\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Linear Systems of Equations \u003c\/b\u003e\u003cb\u003e109\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Direct Methods 110\u003c\/p\u003e \u003cp\u003e4.1.1 LU Factorization of an \u003ci\u003en \u003c\/i\u003e× \u003ci\u003en \u003c\/i\u003eMatrix \u003cb\u003eA \u003c\/b\u003e113\u003c\/p\u003e \u003cp\u003e4.2 Iterative Methods 115\u003c\/p\u003e \u003cp\u003e4.2.1 Jacobi Iteration 115\u003c\/p\u003e \u003cp\u003e4.2.2 Convergence Criterion 116\u003c\/p\u003e \u003cp\u003e4.2.3 Gauss–Seidel Iteration 117\u003c\/p\u003e \u003cp\u003e4.2.4 The Successive Over-Relaxation Method (S.O.R.) 119\u003c\/p\u003e \u003cp\u003e4.2.5 Abstraction of Iterative Methods 120\u003c\/p\u003e \u003cp\u003e4.2.5.1 Questions 120\u003c\/p\u003e \u003cp\u003e4.2.6 Jacobi’s Method 120\u003c\/p\u003e \u003cp\u003e4.2.7 Gauss–Seidel’s Method 121\u003c\/p\u003e \u003cp\u003e4.2.7.1 Relaxation 121\u003c\/p\u003e \u003cp\u003e4.3 Exercises 122\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Two-Point Boundary Value Problems \u003c\/b\u003e\u003cb\u003e125\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 The Finite Element Method (FEM) 125\u003c\/p\u003e \u003cp\u003e5.2 Error Estimates in the Energy Norm 127\u003c\/p\u003e \u003cp\u003e5.2.1 Adaptivity 132\u003c\/p\u003e \u003cp\u003e5.3 FEM for Convection–Diffusion–Absorption BVPs 132\u003c\/p\u003e \u003cp\u003e5.4 Exercises 140\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Scalar Initial Value Problems \u003c\/b\u003e\u003cb\u003e147\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Solution Formula and Stability 147\u003c\/p\u003e \u003cp\u003e6.2 Finite Difference Methods for IVP 149\u003c\/p\u003e \u003cp\u003e6.3 Galerkin Finite Element Methods for IVP 151\u003c\/p\u003e \u003cp\u003e6.3.1 The Continuous Galerkin Method 152\u003c\/p\u003e \u003cp\u003e6.3.1.1 The cG(1) Algorithm 154\u003c\/p\u003e \u003cp\u003e6.3.1.2 The cG(\u003ci\u003eq\u003c\/i\u003e) Method 154\u003c\/p\u003e \u003cp\u003e6.3.2 The Discontinuous Galerkin Method 155\u003c\/p\u003e \u003cp\u003e6.4 A Posteriori Error Estimates 156\u003c\/p\u003e \u003cp\u003e6.4.1 A Posteriori Error Estimate for cG(1) 156\u003c\/p\u003e \u003cp\u003e6.4.1.1 The Dual Problem 157\u003c\/p\u003e \u003cp\u003e6.4.2 A Posteriori Error Estimate for dG(0) 161\u003c\/p\u003e \u003cp\u003e6.4.3 Adaptivity for dG(0) 163\u003c\/p\u003e \u003cp\u003e6.4.3.1 An Adaptivity Algorithm 163\u003c\/p\u003e \u003cp\u003e6.5 A Priori Error Analysis 164\u003c\/p\u003e \u003cp\u003e6.5.1 A Priori Error Estimates for the dG(0) Method 164\u003c\/p\u003e \u003cp\u003e6.6 The Parabolic Case (\u003ci\u003ea\u003c\/i\u003e(\u003ci\u003et\u003c\/i\u003e) ≥ 0) 168\u003c\/p\u003e \u003cp\u003e6.6.1 An Example of Error Estimate 171\u003c\/p\u003e \u003cp\u003e6.7 Exercises 173\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Initial Boundary Value Problems in 1\u003ci\u003ed \u003c\/i\u003e\u003c\/b\u003e\u003cb\u003e177\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 The Heat Equation in 1\u003ci\u003ed \u003c\/i\u003e177\u003c\/p\u003e \u003cp\u003e7.1.1 Stability Estimates 179\u003c\/p\u003e \u003cp\u003e7.1.2 FEM for the Heat Equation 183\u003c\/p\u003e \u003cp\u003e7.1.3 Error Analysis 186\u003c\/p\u003e \u003cp\u003e7.1.4 Exercises 192\u003c\/p\u003e \u003cp\u003e7.2 The Wave Equation in 1\u003ci\u003ed \u003c\/i\u003e193\u003c\/p\u003e \u003cp\u003e7.2.1 Wave Equation as a System of Hyperbolic PDEs 194\u003c\/p\u003e \u003cp\u003e7.2.2 The Finite Element Discretization Procedure 195\u003c\/p\u003e \u003cp\u003e7.2.3 Exercises 197\u003c\/p\u003e \u003cp\u003e7.3 Convection–Diffusion Problems 199\u003c\/p\u003e \u003cp\u003e7.3.1 Finite Element Method 202\u003c\/p\u003e \u003cp\u003e7.3.2 The Streamline-Diffusion Method (SDM) 203\u003c\/p\u003e \u003cp\u003e7.3.3 Exercises 205\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Approximation in Several Dimensions \u003c\/b\u003e\u003cb\u003e207\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 207\u003c\/p\u003e \u003cp\u003e8.2 Piecewise Linear Approximation in 2\u003ci\u003ed \u003c\/i\u003e209\u003c\/p\u003e \u003cp\u003e8.2.1 Basis Functions for the Piecewise Linears in 2\u003ci\u003ed \u003c\/i\u003e209\u003c\/p\u003e \u003cp\u003e8.3 Constructing Finite Element Spaces 216\u003c\/p\u003e \u003cp\u003e8.4 The Interpolant 219\u003c\/p\u003e \u003cp\u003e8.4.1 Error Estimates for Piecewise Linear Interpolation 222\u003c\/p\u003e \u003cp\u003e8.5 The \u003ci\u003eL\u003c\/i\u003e2(Revisited) and Ritz Projections 228\u003c\/p\u003e \u003cp\u003e8.5.1 The Ritz or Elliptic Projection 230\u003c\/p\u003e \u003cp\u003e8.6 Exercises 231\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 The Boundary Value Problems in \u003c\/b\u003e\u003cb\u003eℝ\u003ci\u003eN \u003c\/i\u003e\u003c\/b\u003e\u003cb\u003e235\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 The Poisson Equation 235\u003c\/p\u003e \u003cp\u003e9.1.1 Weak Stability 236\u003c\/p\u003e \u003cp\u003e9.1.2 Error Estimates for the CG(1) FEM 237\u003c\/p\u003e \u003cp\u003e9.1.3 Proof of the Regularity Lemma 242\u003c\/p\u003e \u003cp\u003e9.2 Stationary Convection–Diffusion Equation 243\u003c\/p\u003e \u003cp\u003e9.2.1 The Elliptic Case 243\u003c\/p\u003e \u003cp\u003e9.2.1.1 A Brief Note on Distributions 244\u003c\/p\u003e \u003cp\u003e9.2.2 Error Estimates 248\u003c\/p\u003e \u003cp\u003e9.3 Hyperbolicity Features 249\u003c\/p\u003e \u003cp\u003e9.3.1 Convection Dominating Case 250\u003c\/p\u003e \u003cp\u003e9.3.2 The SD Method for Convection Diffusion Problem 251\u003c\/p\u003e \u003cp\u003e9.3.3 Stability Estimates 252\u003c\/p\u003e \u003cp\u003e9.3.4 Error Estimates for Convention Dominating in 2\u003ci\u003ed \u003c\/i\u003e252\u003c\/p\u003e \u003cp\u003e9.4 Exercises 255\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 The Initial Boundary Value Problems in \u003c\/b\u003e\u003cb\u003eℝ\u003ci\u003eN \u003c\/i\u003e\u003c\/b\u003e\u003cb\u003e261\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 The Heat Equation in ℝ\u003cb\u003e\u003ci\u003eN\u003c\/i\u003e\u003c\/b\u003e261\u003c\/p\u003e \u003cp\u003e10.1.1 The Fundamental Solution 262\u003c\/p\u003e \u003cp\u003e10.1.2 Stability 263\u003c\/p\u003e \u003cp\u003e10.1.3 The Finite Element for Heat Equation 265\u003c\/p\u003e \u003cp\u003e10.1.3.1 The Semidiscrete Problem 265\u003c\/p\u003e \u003cp\u003e10.1.4 A Fully Discrete Algorithm 269\u003c\/p\u003e \u003cp\u003e10.1.5 The Discrete Equations 270\u003c\/p\u003e \u003cp\u003e10.1.6 A Priori Error Estimate: Fully Discrete Problem 271\u003c\/p\u003e \u003cp\u003e10.2 The Wave Equation in ℝ\u003ci\u003ed \u003c\/i\u003e272\u003c\/p\u003e \u003cp\u003e10.2.1 The Weak Formulation 273\u003c\/p\u003e \u003cp\u003e10.2.2 The Semidiscrete Problem 273\u003c\/p\u003e \u003cp\u003e10.2.2.1 A Priori Error Estimates for the Semidiscrete Problem 274\u003c\/p\u003e \u003cp\u003e10.2.3 The Fully Discrete Problem 275\u003c\/p\u003e \u003cp\u003e10.2.3.1 Finite Elements for the Fully Discrete Problem 276\u003c\/p\u003e \u003cp\u003e10.2.4 Error Estimate for cG(1) 278\u003c\/p\u003e \u003cp\u003e10.3 Exercises 279\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix A Answers to Some Exercises \u003c\/b\u003e\u003cb\u003e285\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 1. Exercise Section 1.4.1 285\u003c\/p\u003e \u003cp\u003eChapter 1. Exercise Section 1.5.4 285\u003c\/p\u003e \u003cp\u003eChapter 2. Exercise Section 2.11 286\u003c\/p\u003e \u003cp\u003eChapter 3. Exercise Section 3.5 286\u003c\/p\u003e \u003cp\u003eChapter 3. Exercise Section 3.8 287\u003c\/p\u003e \u003cp\u003eChapter 4. Exercise Section 4.3 288\u003c\/p\u003e \u003cp\u003eChapter 5. Exercise Section 5.4 289\u003c\/p\u003e \u003cp\u003eChapter 6. Exercise Section 6.7 291\u003c\/p\u003e \u003cp\u003eChapter 7. Exercise Section 7.2.3 292\u003c\/p\u003e \u003cp\u003eChapter 7. Exercise Section 7.3.3 292\u003c\/p\u003e \u003cp\u003eChapter 9. Poisson Equation. Exercise Section 9.4 292\u003c\/p\u003e \u003cp\u003eChapter 10. IBVPs: Exercise Section 10.3 293\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix B Algorithms and Matlab Codes \u003c\/b\u003e\u003cb\u003e295\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eB.1 A Matlab Code to Compute the Mass Matrix \u003cb\u003eM \u003c\/b\u003efor a Nonuniform Mesh 296\u003c\/p\u003e \u003cp\u003eB.1.1 A Matlab Routine to Compute the Load Vector \u003cb\u003eb \u003c\/b\u003e297\u003c\/p\u003e \u003cp\u003eB.2 Matlab Routine to Compute the \u003ci\u003eL\u003c\/i\u003e2-Projection 298\u003c\/p\u003e \u003cp\u003eB.2.1 A Matlab Routine for the Composite Midpoint Rule 299\u003c\/p\u003e \u003cp\u003eB.2.2 A Matlab Routine for the Composite Trapezoidal Rule 299\u003c\/p\u003e \u003cp\u003eB.2.3 A Matlab Routine for the Composite Simpson’s Rule 299\u003c\/p\u003e \u003cp\u003eB.3 A Matlab Routine Assembling the Stiffness Matrix 300\u003c\/p\u003e \u003cp\u003eB.4 A Matlab Routine to Assemble the Convection Matrix 301\u003c\/p\u003e \u003cp\u003eB.5 Matlab Routine for Forward-, Backward-Euler, and Crank–Nicolson 302\u003c\/p\u003e \u003cp\u003eB.6 A Matlab Routine for Mass-Matrix in 2\u003ci\u003ed \u003c\/i\u003e304\u003c\/p\u003e \u003cp\u003eB.7 A Matlab Routine for a Poisson Assembler in 2\u003ci\u003ed \u003c\/i\u003e304\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix C Sample Assignments \u003c\/b\u003e\u003cb\u003e307\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eC.1 Assignment 1 307\u003c\/p\u003e \u003cp\u003eC.2 Assignment 2 308\u003c\/p\u003e \u003cp\u003eC.2.1 Grading Policy of the Assignment 308\u003c\/p\u003e \u003cp\u003eC.2.2 Theory 308\u003c\/p\u003e \u003cp\u003eC.2.3 Selected Applications 309\u003c\/p\u003e \u003cp\u003eC.2.3.1 Convection–Diffusion–Absorption\/Reaction 309\u003c\/p\u003e \u003cp\u003eC.2.3.2 Electrostatics 310\u003c\/p\u003e \u003cp\u003eC.2.3.3 2\u003ci\u003ed \u003c\/i\u003eFluid Flow 310\u003c\/p\u003e \u003cp\u003eC.2.3.4 Heat Conduction 310\u003c\/p\u003e \u003cp\u003eC.2.3.5 Quantum Physics 310\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix D Symbols \u003c\/b\u003e\u003cb\u003e313\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eD.1 Table of Symbols 313\u003c\/p\u003e \u003cp\u003eBibliography 317\u003c\/p\u003e \u003cp\u003eIndex 327\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand New","offer_id":52428657787160,"sku":"9781119671640","price":88.39,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781119671640.jpg?v=1784683564","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/an-introduction-to-the-finite-element-method-for-differential-equations-hardback-9781119671640","provider":"Freshly Printed Books","version":"1.0","type":"link"}