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Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods

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Title: Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods
Author: Kaliakin, Victor N.
ISBN: 082470679X / 9780824706791
Format: Hard Cover
Pages: 664
Publisher: Marcel Dekker
Year: 2002
Availability: 2 to 3 weeks
     
 
  • Description
  • Contents

This reference/text focuses on classical approximate solution techniques such as the finite difference method, the method of weighted residuals, and variation methods, culminating in an introduction to the finite element method (FEM)-discussing the general notion of approximate solutions and associated errors.

With 1500 equations and more than 750 references, drawings, and tables, Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods describes the approximate solution of ordinary and partial differential equations using the finite difference method....covers the method of weighted residuals....considers variational methods.......highlights all aspects associated with the formulation of finite element equations......outlines meshing of the solution domain, modal specifications, solution of global equations, solution refinement, and assessment of results.....focuses on interpolation functions for one-, two-, and three-dimensional elements....analyzes element mapping....examines scalar field problems.....spotlights application of the FEM to elastostatic problems.....details meshing schemes and guidelines for developing correct mathematical models.....showcases general programming aspects associated with the FEM...and more.

Preface
Acknowledgements
Glossary of Notations and Units

Chapter 1 : Governing Equations and Their Approximate Solution
Chapter 2 : Computer Storage and Manipulation of Numbers
Chapter 3 : The Finite Difference Method
Chapter 4 : The Method of Weighted Residuals
Chapter 5 : Variational Methods
Chapter 6 : Introduction to the Finite Element Method
Chapter 7 : Development of Finite Element Equations
Chapter 8 : Steps in Performing Finite Element Analyses
Chapter 9 : Element Interpolation Functions
Chapter 10 : Element Mapping
Chapter 11 : Finite Element Analysis of Scalar Field Problems
Chapter 12 : Finite Element Analysis in Linear Elastostatics
Chapter 13 : Implementation, Modeling, and Related Issues

A : Mathematical Potpourri
B : Some Notes on Heat Flow
C : Local and Natural Coordinate Systems
D : The Patch Test
E : Solution of Linear Systems of Equations
F : Notes on Integration of Finite Elements
References
Index

 
 
 
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