Description

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 * Complete with homework exercises and supporting website with instructor's solutions manual

Readership

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

Preface

Features of the text and accompanying resources

Notation

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

Details

No. of pages:
512
Language:
English
Copyright:
© 2005
Published:
Imprint:
Butterworth-Heinemann
Print ISBN:
9780750667227
Electronic ISBN:
9780080472751