Finite Element Analysis with Error Estimators

1st Edition

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

Authors: J. Akin
Paperback ISBN: 9780750667227
eBook ISBN: 9780080472751
Imprint: Butterworth-Heinemann
Published Date: 22nd June 2005
Page Count: 512
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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.

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


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

Table of Contents


Features of the text and accompanying resources


Chapter 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 section-titles

1.6 Exercises

Chapter 2: Mathematical preliminaries

2.1 Introduction

2.2 Linear spaces and norms

2.3 Sobolev norms *

2.4 Dual problem, self-adjointness

2.5 Weighted residuals

2.6 Boundary condition 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 Eigen-problems

2.18 Equivalent forms *

2.19 Exercises

Chapter 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 Hierarchical interpolation

3.7 Space-time interpolations*

3.8 Nodally exact interpolations *

3.9 Interpolation error *

3.10 Gradient estimates *

3.11 Exercises

Chapter 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

Chapter 5: Error estimates for elliptic problems

5.1 Introduction

5.2 Error estimates

5.3 Hierarchical error indicator

5.4 Flux balancing error estimates


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© Butterworth-Heinemann 2005
eBook ISBN:
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About the Author

J. Akin

Affiliations and Expertise

Professor of Mechanical Engineering, Rice University, Houston, TX