Finite Element Methods: A Practical Guide

✍ Scribed by Jonathan Whiteley (auth.)

• Publisher: Springer International Publishing
• Year: 2017
• Tongue: English
• Leaves: 236
• Series: Mathematical Engineering
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xi
An Overview of the Finite Element Method....Pages 1-4
A First Example....Pages 5-23
Linear Boundary Value Problems....Pages 25-53
Higher Order Basis Functions....Pages 55-80
Nonlinear Boundary Value Problems....Pages 81-101
Systems of Ordinary Differential Equations....Pages 103-118
Linear Elliptic Partial Differential Equations....Pages 119-141
More General Elliptic Problems....Pages 143-160
Quadrilateral Elements....Pages 161-173
Higher Order Basis Functions....Pages 175-188
Nonlinear Elliptic Partial Differential Equations....Pages 189-196
Systems of Elliptic Equations....Pages 197-202
Parabolic Partial Differential Equations....Pages 203-209
Back Matter....Pages 211-232

✦ Subjects

Structural Mechanics;Partial Differential Equations;Numerical Analysis;Mathematical Modeling and Industrial Mathematics;Appl.Mathematics/Computational Methods of Engineering