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Finite Element Methods

A Practical Guide

  • Book
  • © 2017

Overview

Authors:
  1. Jonathan Whiteley

    1. Department of Computer Science, University of Oxford, Oxford, United Kingdom

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  • Provides a practical guide to the finite element method
  • Covers different classes of meshes and basis functions
  • Requires only little prerequisites without lacking mathematical rigour
  • Treats both linear and nonlinear partial differential equations
  • Includes supplementary material: sn.pub/extras

Part of the book series: Mathematical Engineering (MATHENGIN)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. An Overview of the Finite Element Method

    • Jonathan Whiteley
    Pages 1-4

  3. A First Example

    • Jonathan Whiteley
    Pages 5-23

  4. Linear Boundary Value Problems

    • Jonathan Whiteley
    Pages 25-53

  5. Higher Order Basis Functions

    • Jonathan Whiteley
    Pages 55-80

  6. Nonlinear Boundary Value Problems

    • Jonathan Whiteley
    Pages 81-101

  7. Systems of Ordinary Differential Equations

    • Jonathan Whiteley
    Pages 103-118

  8. Linear Elliptic Partial Differential Equations

    • Jonathan Whiteley
    Pages 119-141

  9. More General Elliptic Problems

    • Jonathan Whiteley
    Pages 143-160

  10. Quadrilateral Elements

    • Jonathan Whiteley
    Pages 161-173

  11. Higher Order Basis Functions

    • Jonathan Whiteley
    Pages 175-188

  12. Nonlinear Elliptic Partial Differential Equations

    • Jonathan Whiteley
    Pages 189-196

  13. Systems of Elliptic Equations

    • Jonathan Whiteley
    Pages 197-202

  14. Parabolic Partial Differential Equations

    • Jonathan Whiteley
    Pages 203-209

  15. Back Matter

    Pages 211-232
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Keywords

About this book

This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.

Authors and Affiliations

  • Department of Computer Science, University of Oxford, Oxford, United Kingdom

    Jonathan Whiteley

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