A Finite Element Primer for Beginners: The Basics

✍ Scribed by Tarek I. Zohdi (auth.)

• Publisher: Springer International Publishing
• Year: 2015
• Tongue: English
• Leaves: 113
• Series: SpringerBriefs in Applied Sciences and Technology
• Edition: 1
• Category: Library

✦ Synopsis

The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are:

(1) Weighted residual methods and Galerkin approximations,

(2) A model problem for one-dimensional linear elastostatics,

(3) Weak formulations in one dimension,

(4) Minimum principles in one dimension,

(5) Error estimation in one dimension,

(5) Construction of Finite Element basis functions in one dimension,

(6) Gaussian Quadrature,

(7) Iterative solvers and element by element data structures,

(8) A model problem for three-dimensional linear elastostatics,

(9) Weak formulations in three dimensions,

(10) Basic rules for element construction in three-dimensions,

(11) Assembly of the system and solution schemes,

(12) Assembly of the system and solution schemes,

(13) An introduction to time-dependent problems and

(14) A brief introduction to rapid computation based on domain decomposition and basic parallel processing.

✦ Table of Contents

Front Matter....Pages i-ix
Weighted Residuals and Galerkin’s Method for a Generic 1-D Problem....Pages 1-4
A Model Problem: 1-D Elastostatics....Pages 5-11
A Finite Element Implementation in One Dimension....Pages 13-28
Accuracy of the Finite Element Method....Pages 29-36
Element-by-Element Iterative Solution Schemes....Pages 37-43
Weak Formulations in Three Dimensions....Pages 45-50
A Finite Element Implementation in Three Dimensions....Pages 51-68
Accuracy of the Finite Element Method....Pages 69-74
Time-Dependent Problems....Pages 75-79
Summary and Advanced Topics....Pages 81-84
Back Matter....Pages 85-108

✦ Subjects

Continuum Mechanics and Mechanics of Materials; Engineering Fluid Dynamics; Complexity; Computational Science and Engineering; Mathematical Modeling and Industrial Mathematics; Numerical and Computational Physics