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Finite Element Analysis with Error Estimators

Finite Element Analysis with Error Estimators, 1st Edition

An Introduction to the FEM and Adaptive Error Analysis for Engineering Students

Finite Element Analysis with Error Estimators, 1st Edition,J. Akin,ISBN9780750667227






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The first automatic adaptation text for engineers

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Key Features

* The only introductory FEA text with error estimation for students of engineering, scientific computing and applied mathematics
* Includes source code for creating and proving FEA error estimators
* Complete with homework exercises and supporting website with instructor's solutions manual


This key text is written for senior undergraduate and graduate engineering students. It delivers a complete introduction to finite element methods and to automatic adaptation (error estimation) that will enable students to understand and use FEA as a true engineering tool. It has been specifically developed to be accessible to non-mathematics students and provides the only complete text for FEA with error estimators for non-mathematicians. Error estimation is taught on nearly half of all FEM courses for engineers at senior undergraduate and postgraduate level; no other existing textbook for this market covers this topic.


Senior undergraduate and masters level courses in engineering, computational science, and some applied mathematics programs. Most aerospace, chemical, civil & mechanical engineering programs, & senior level electrical engineering courses

J. Akin

Affiliations and Expertise

Professor of Mechanical Engineering, Rice University, Houston, TX

Finite Element Analysis with Error Estimators, 1st Edition

1. Introduction
1.1 Finite Element Methods
1.2 Capabilities of FEA
1.3 Outline of Finite Element Procedures
1.4 Assembly into the System Equations
1.5 Error Concepts
1.6 Exercises
1.7 Bibliography
2. Mathematical Preliminaries
2.1 Introduction
2.2 Linear Spaces and Norms
2.3 Sobolev Norms
2.4 Dual Problems, Self-Adjointness
2.5 Weighted Residuals
2.6 Boundary Conditions Terms
2.7 Adding More Unknowns
2.8 Numerical Integration
2.9 Integration By Parts
2.10 Finite Element Model Problem
2.11 Continuous Nodal Flux Recovery
2.12 A One-Dimensional Example Error Analysis
2.13 General Boundary Condition Choices
2.14 General Matrix Partitions
2.15 Elliptic Boundary Value Problems
2.16 Initial Value Problems
2.17 Equivalent Forms
2.18 Exercises
2.19 Bibliography
3. Element Interpolation and Local Coordinates
3.1 Introduction
3.2 Linear Interpolation
3.3 Quadratic Interpolation
3.4 Lagrange Interpolation
3.5 Hermitian Interpolation
3.6 Hierarchal Interpolation
3.7 Space-Time Interpolation
3.8 Nodally Exact Interpolations
3.9 Interpolation Error
3.10 Gradient Estimates
3.11 Exercises
3.12 Bibliography
4. One-Dimensional Integration
4.1 Introduction
4.2 Local Coordinate Jacobian
4.3 Exact Polynomial Integration
4.4 Numerical Integration
4.5 Variable Jacobians
4.6 Exercises
4.7 Bibliography
5. Error Estimation for Elliptic Problems
5.1 Introduction
5.2 Error Estimates
5.3 Hierarchical Error Indicator
5.4 Flux Balancing Methods
5.5 Element Adaptivity
5.6 H Adaptivity
5.7 P Adaptivity
5.8 HP Adaptivity
5.9 Exercises
5.10 Bibliography
6. Super-convergent Patch Recovery
6.1 Patch Implementation Database
6.2 SCP Nodal Flux Averaging
6.3 Computing the SCP Element Error Estimate
6.4 Hessian Matrix
6.5 Bibliography
7. Variational Methods
7.1 Introduction
7.2 Structural Mechanics
7.3 Finite Element Analysis
7.4 Continuous Elastic Bar
7.5 Thermal Loads on a Bar
7.6 Reaction Flux Recovery for an Element
7.7 Heat Transfer in a Rod
7.8 Element Validation
7.9 Euler’s Equations of Variational Calculus
7.10 Exercises
7.11 Bibliography
8. Cylindrical Analysis Problems
8.1 Introduction
8.2 Heat Conduction in a Cylinder
8.3 Cylindrical Stress Analysis
8.4 Exercises
8.4 Bibliography
9. General Interpolation
9.1 Introduction
9.2 Unit Coordinate Interpolation
9.3 Natural Coordinates
9.4 Isoparametric and Subparametric Elements
9.5 Hierarchical Interpolation
9.6 Differential Geometry
9.7 Mass Properties
9.9 Interpolation Error
9.9 Element Distortions
9.10 Space-Time Interpolation
9.11 Exercises
9.12 Bibliography
10. Integration Methods
10.1 Introduction
10.2 Unit Coordinate Integration
10.3 Simplex Coordinate Integration
10.4 Numerical Integration
10.5 Typical Source Distribution Integrals
10.6 Minimal, Optimal, Reduced and Selected Integration
10.7 Exercises
10.8 Bibliography
11. Scalar Fields
11.1 Introduction
11.2 Variational Formulation
11.3 Element and Boundary Matrices
11.4 Linear Triangle Element
11.5 Linear Triangle Applications
11.6 Bilinear Rectangulars
11.7 General 2-D Elements
11.8 Numerically Integrated Arrays
11.9 Strong Diagonal Gradient SCP Test Case
11.10 Orthtropic Conduction
11.11 Axisymmetric Formulations
11.12 Torsion
11.13 Introduction to Linear Flows
11.14 Potential Flow
11.15 Axisymmetric Plasma Equilibria
11.16 Slider Bearing Lubrication
11.17 Transient Scalar Fields
11.18 Exercises
11.19 Bibliography
12. Vector Fields
12.1 Introduction
12.2 Displacement Based Stress Analysis
12.3 Planar Models
12.3.1 Minimum Total Potential Energy
12.3.2 Displacement Interpolations
12.3.3 Strain-Displacement Relations
12.3.4 Stress-Strain Law
12.4 Matrices for the Constant Strain Triangle
12.5 Stress and Strain Transformations
12.6 Axisymmetric Solid Stress
12.7 General Solid Stress
12.8 Anisotropic Materials
12.9 Circular Hole in an Infinite Plate
12.10 Exercises
12.11 Bibliography

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