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Table of Contents
Preface; Contents; 1 Weighted Residuals and Galerkin''s Method for a Generic 1-D Problem; 1.1 Introduction: Weighted Residual Methods ; 1.2 Galerkin''s Method; 1.3 An Overall Framework ; 2 A Model Problem: 1-D Elastostatics; 2.1 Introduction: A Model Problem; 2.2 Weak Formulations in One Dimension; 2.3 An Example; 2.4 Some Restrictions; 2.5 Remarks on Nonlinear Problems; References; 3 A Finite Element Implementation in One Dimension; 3.1 Introduction; 3.2 Finite Element Method Implementation; 3.3 FEM Approximation; 3.4 Construction of FEM Basis Functions.
3.5 Integration and Gaussian Quadrature3.5.1 An Example; 3.6 Global/Local Transformations; 3.7 Differential Properties of Shape Functions; 3.8 Postprocessing; 3.9 A Detailed Example; 3.9.1 Weak Form; 3.9.2 Formation of the Discrete System; 3.9.3 Applying Boundary Conditions; 3.9.4 Massive Data Storage Reduction; 3.10 Quadratic Elements; Reference; 4 Accuracy of the Finite Element Method; 4.1 Introduction ; 4.2 The ``Best Approximation'''' Theorem ; 4.3 An Error Bound; 4.4 The Principle of Minimum Potential Energy ; 4.5 Simple Estimates for Adequate FEM Meshes ; 4.6 Local Mesh Refinement.
7.6 Three-Dimensional Shape Functions7.7 Differential Properties of Shape Functions; 7.8 Differentiation in the Referential Coordinates; 7.8.1 Implementation Issues; 7.8.2 An Example of the Storage Scaling; 7.9 Surface Jacobians and Nanson''s Formula; 7.10 Postprocessing; References; 8 Accuracy of the Finite Element Method; 8.1 Introduction; 8.2 The ``Best Approximation'''' Theorem; 8.3 A Bound on the Error; 8.4 Simple Estimates for Adequate FEM Meshes
Revisited for Three Dimensions; 8.5 Local Error Estimation and Adaptive Mesh Refinement; 8.5.1 A Posteriori Recovery Methods.
8.5.2 A Posteriori Residual MethodsReferences; 9 Time-Dependent Problems; 9.1 Introduction; 9.2 Generic Time Stepping; 9.3 Application to the Continuum Formulation; References; 10 Summary and Advanced Topics; References; Appendix AElementary Mathematical Concepts; Appendix BBasic Continuum Mechanics; Appendix CConvergence of Recursive Iterative Schemes.
3.5 Integration and Gaussian Quadrature3.5.1 An Example; 3.6 Global/Local Transformations; 3.7 Differential Properties of Shape Functions; 3.8 Postprocessing; 3.9 A Detailed Example; 3.9.1 Weak Form; 3.9.2 Formation of the Discrete System; 3.9.3 Applying Boundary Conditions; 3.9.4 Massive Data Storage Reduction; 3.10 Quadratic Elements; Reference; 4 Accuracy of the Finite Element Method; 4.1 Introduction ; 4.2 The ``Best Approximation'''' Theorem ; 4.3 An Error Bound; 4.4 The Principle of Minimum Potential Energy ; 4.5 Simple Estimates for Adequate FEM Meshes ; 4.6 Local Mesh Refinement.
7.6 Three-Dimensional Shape Functions7.7 Differential Properties of Shape Functions; 7.8 Differentiation in the Referential Coordinates; 7.8.1 Implementation Issues; 7.8.2 An Example of the Storage Scaling; 7.9 Surface Jacobians and Nanson''s Formula; 7.10 Postprocessing; References; 8 Accuracy of the Finite Element Method; 8.1 Introduction; 8.2 The ``Best Approximation'''' Theorem; 8.3 A Bound on the Error; 8.4 Simple Estimates for Adequate FEM Meshes
Revisited for Three Dimensions; 8.5 Local Error Estimation and Adaptive Mesh Refinement; 8.5.1 A Posteriori Recovery Methods.
8.5.2 A Posteriori Residual MethodsReferences; 9 Time-Dependent Problems; 9.1 Introduction; 9.2 Generic Time Stepping; 9.3 Application to the Continuum Formulation; References; 10 Summary and Advanced Topics; References; Appendix AElementary Mathematical Concepts; Appendix BBasic Continuum Mechanics; Appendix CConvergence of Recursive Iterative Schemes.