LEADER 05579nam 22007693u 450 001 9911006699703321 005 20230803040151.0 010 $a9781523125074 010 $a1523125071 010 $a9780486318011 010 $a048631801X 035 $a(CKB)3710000000318841 035 $a(EBL)1897371 035 $a(SSID)ssj0001117099 035 $a(PQKBManifestationID)12435558 035 $a(PQKBTitleCode)TC0001117099 035 $a(PQKBWorkID)11099476 035 $a(PQKB)11725545 035 $a(MiAaPQ)EBC1897371 035 $a(Au-PeEL)EBL1897371 035 $a(CaONFJC)MIL563839 035 $a(OCoLC)868280599 035 $a(MiAaPQ)EBC7294290 035 $a(Au-PeEL)EBL7294290 035 $a(Perlego)112478 035 $a(OCoLC)1402814293 035 $a(EXLCZ)993710000000318841 100 $a20141222d2013|||| u|| | 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFinite Elements and Approximation 205 $a1st ed. 210 $aNewburyport $cDover Publications$d2013 215 $a1 online resource (574 p.) 225 1 $aDover Books on Engineering 300 $aDescription based upon print version of record. 311 08$a9780486453019 311 08$a0486453014 327 $aCover; Title Page; Copyright Page; Table of Contents; 1. Continuum Boundary Value Problems and The Need for Numerical Discretization. Finite Difference Methods; 1.1. Introduction,; 1.2. Some Examples of Continuum Problems,; 1.3. Finite Differences in One Dimension,; 1.4. Derivative Boundary Conditions,; 1.5. Nonlinear Problems,; 1.6. Finite Differences in More Than One Dimension,; 1.7. Problems Involving Irregularly Shaped Regions,; 1.8. Nonlinear Problems in More Than One Dimension,; 1.9. Approximation and Convergence,; 1.10. Concluding Remarks,; References,; Suggested Further Reading, 327 $a2. Weighted Residual Methods: Use of Continuous Trial Functions2.1. Introduction-Approximation by Trial Functions,; 2.2. Weighted Residual Approximations,; 2.3. Approximation to the Solutions of Differential Equations and the Use of Trial Function-Weighted Residual Forms. Boundary Conditions Satisfied by Choice of Trial Functions,; 2.4. Simultaneous Approximation to the Solutions of Differential Equations and to the Boundary Conditions,; 2.5. Natural Boundary Conditions,; 2.6. Boundary Solution Methods,; 2.7. Systems of Differential Equations,; 2.8. Nonlinear Problems, 327 $a2.9. Concluding Remarks,References,; Suggested Further Reading,; 3. Piecewise Defined Trial Functions and The Finite Element Method; 3.1. Introduction-The Finite Element Concept,; 3.2. Some Typical Locally Defined Narrow-Base Shape Functions,; 3.3. Approximation to Solutions of Differential Equations and Continuity Requirements,; 3.4. Weak Formulation and the Galerkin Method,; 3.5. Some One-Dimensional Problems,; 3.6. Standard Discrete System. A Physical Analogue of the Equation Assembly Process,; 3.7. Generalization of the Finite Element Concepts for Two- and Three-Dimensional Problems, 327 $a3.8. The Finite Element Method for Two-Dimensional Heat Conduction Problems,3.9. Two-Dimensional Elastic Stress Analysis Using Triangular Elements,; 3.10. Are Finite Differences a Special Case of the Finite Element Method?,; 3.11. Concluding Remarks,; References,; Suggested Further Reading,; 4. Higher Order Finite Element Approximation; 4.1. Introduction,; 4.2. Degree of Polynomial in Trial Functions and Convergence Rates,; 4.3. The Patch Test,; 4.4. Standard Higher Order Shape Functions for One-Dimensional Elements with C0 Continuity, 327 $a4.5. Hierarchical Forms of Higher Order One-Dimensional Elements with C0 Continuity,4.6. Two-Dimensional Rectangular Finite Element Shape Functions of Higher Order,; 4.7. Two-Dimensional Shape Functions for Triangles,; 4.8. Three-Dimensional Shape Functions,; 4.9. Concluding Remarks,; References,; Suggested Further Reading,; 5. Mapping and Numerical Integration; 5.1. The Concept of Mapping,; 5.2. Numerical Integration,; 5.3. More on Mapping,; 5.4. Mesh Generation and Concluding Remarks,; References,; Suggested Further Reading,; 6. Variational Methods; 6.1. Introduction, 327 $a6.2. Variational Principles, 330 $aA powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o 410 0$aDover Books on Engineering 606 $aApproximation theory 606 $aFinite element method 606 $aEngineering & Applied Sciences$2HILCC 606 $aApplied Mathematics$2HILCC 615 0$aApproximation theory. 615 0$aFinite element method. 615 7$aEngineering & Applied Sciences 615 7$aApplied Mathematics 676 $a511/.4 700 $aZienkiewicz$b O. C$0440603 701 $aMorgan$b K$012722 801 0$bAU-PeEL 801 1$bAU-PeEL 801 2$bAU-PeEL 906 $aBOOK 912 $a9911006699703321 996 $aFinite Elements and Approximation$94390399 997 $aUNINA