# What is the best textbook on finite element modelling?

Finite as finite element modelling may be, the number of books in the library on the subject is certainly not finite. At least that's the way it seemed. Shelves upon shelves of them. I've learnt in the past that some books on the same subject can be orders of magnitude better than others, and it's impossible to tell by their covers.

The aim was to find the highest quality textbooks on finite element analysis. The right choice of book can sometimes save hours later on.

## Contents |

# Results

Looked around the Internet, especially FEM courses at top universities.

The following authors are mentioned often:

- K. J. Bathe — classic.
- J. N. Reddy — introductory.
- Thomas J. R. Hughes — detailed introductory.
- Claes Johnson — introductory.
- Oden and Carey — introductory, higher level.
- Zienkiewicz and Taylor — detailed, wide coverage, not introductory.

It seems that your chances of writing an acclaimed introductory text to finite element analysis are looking good if you work alone, and if one of your initials is J.

Mentioned often, perhaps slightly less:

- Dietrich Braess
- Huebner
- Jacob Fish, Ted Belytschko
- Silvester and Ferrari
- Ivo M. Babuška

## Recommended on Comsol's website

There were also a couple of titles by Zimmerman, recommended on forums for the software I'm using for FEM, called *Comsol*. (Generally they have been referred to as proper books, compared to other Comsol-specific books, which are of the "click here, then click there" variety.) I found one of Zimmerman's books in our library. The section I started reading started off well, but then became confusing, and by the end of it some of the sentences became nonsensical, as if they haven't been proof-read. However, Zimmerman does say that it's not meant to be an introductory book, and recommends J. N. Reddy's text.

## Book by J. N. Reddy

So, naturally, Reddy's was the book I took to read next. It is very good. It goes exactly into the right amount of detail to explain everything. For example, there is a section called *Need for Weighted-Integral Statements*, which demonstrates via an example how adding a weighting function makes the FEM idea mathematically sound, whereas the strong form cannot tolerate the constraints we place on the approximating functions, and leads to an inconsistent algebraic system of equations. It's a crucial insight: if you want to use an approximating scheme, you have to define what you mean by an approximation.

# Source notes

These are scraps of hypertext with mentions of FEM books.

Finite elements: theory, fast solvers, and applications in elasticity theory

Dietrich Braess

J.-L. Guermond, A. Ern: Theory and Practice of Finite Elements

In-depth treatment, in particular part III on FE realization is relevant

J. Fish, T. Belytschko: A First Course in Finite Elements Introductory text from an engineering point of view, almost no realization of FE.

C. Johnson: Numerical Solution of Partial Differential Equations by
the Finite Element Method

Classic introductory textbook.

H.R. Schwarz: Finite Element Methods

Classic textbook.

The Finite Element Method for Elliptic Problems (Classics in Applied
Mathematics) [Paperback]

Philippe G. Ciarlet (Author)

The Finite Element Method: Its Basis and Fundamentals, 6th Edition

By O. C. Zienkiewicz, R. L. Taylor & J.Z. Zhu

+2+1+1 -1

"Numerical Treatment of Partial Differential Equations" by Grossmann and Ross

"Numerical Solution of Partial Differential Equations by the Finite Element Method" by Claes Johnson

Programming the Finite Element Method [Paperback]

Ian M. Smith (Author), D. V. Griffiths (Author)

Reddy's Introduction to the FEM

"The Finite Element Method: Linear Static and Dynamic Finite Element
Analysis" by Thomas J. R. Hughes

+1

Brenner and Scott

Finite Element Method for Electrical Engineering by P.P. Sylvester and
.... Ferrari

+1

FEM for electromagnetics by Volakis, Chatterjee and Kempel

"The finite element methods in electromagnetics" by Jianming Jin

Numerical Recipes cites Strang and Fix, Mitchell and Griffiths (something tells me this is likely to be a good read), and Burnett with respect to FEM, but these are all titles from the 1980s and earlier.

## University courses textbooks

### Stanford

Becker, E. B. G. F. Carey, and J. T. Oden, Finite Elements an Introduction , Texas Institute for Computational Mechanics, UT Austin, 1981

### MIT

Bathe, K. J. Finite Element Procedures. Cambridge, MA: Klaus-Jurgen Bathe, 2007. ISBN: 9780979004902.

(Book by lecturer)

### Rensselaer

48 titles listed but course homepage is outdated by over a decade.

### Queensland

Liu, G.R. and Quek, S.S., 2003. The Finite Element Method, a Practical Course, Butterworth/Heinemann, Oxford.

### Wayne State

Dietrich Braess, Finite Elements: Theory, fast solvers, and applications in solid mechanics, Cambridge University Press, New York, 1997. ISBN 0-521-58834-0

Susanne C. Brenner and L. Ridgway Scott: The Mathematical Theory of Finite Element Methods, Springer-Verlag, New York, 1994. ISBN 0-387-94193-2

Claes Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method, Cambridge University Press, Cambridge, 1987. ISBN 0-521-34758-0

Christoph Schwab, p- and hp-Finite Element Methods: Theory and applications in solid and fluid mechanics, Numerical Mathematics and Scientific Computation. The Clarendon Press, Oxford University Press, New York, 1998. xii+374 pp. ISBN 0-19-850390-3

Barna Szabo and Ivo Babuska: Finite Element Analysis, John-Wiley & Sons, New York, 1991. ISBN 0-471-50273-1

### Berkeley

46 titles in bibliography, but the following items are in reserve (high-volume use):

K.H. Huebner, D.L. Dewhirst, D.E. Smith, and T.G. Byrom. The Finite Element Method for Engineers.

O.C. Zienkiewicz, R.L. Taylor, and J.Z. Zhu. The Finite Element Method; Its Basis and Fundamentals.

J.N. Reddy. An Introduction to the Finite Element Method.

G. Strang and G.J. Fix. An Analysis of the Finite Element Method.

J.T. Oden and G.F. Carey. Finite Elements: Mathematical Aspects

C. Johnson. Numerical Solution of Partial Differential Equations by the Finite Element Method.

D. Braess. Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics.

E.B. Becker, G.F. Carey, and J.T. Oden. Finite Elements: an Introduction,

G.F. Carey and J.T. Oden. Finite Elements: a Second Course

G.F. Carey and J.T. Oden. Finite Elements: Computational Aspects

T.J.R. Hughes. The Finite Element Method; Linear Static and Dynamic Finite Element Analysis.

### Cornell

J. N. Reddy, An introduction to the finite element method (2005).

K. H. Huebner, D. L. Dewhirst, D. E. Smith, T. G. Byrom, The Finite Element Method for Engineers (2001).

J. Fish and T. Belytschko, A First Course in Finite Elements (Paperback) (2007).

J. T. Oden, E. B. Becker, G. F. Carey, Finite Elements: An Introduction. Volume I (1981).

K.-J. Bathe, Finite Element Procedures (Part 1-2) (Paperback) (1995).

O. C. Zienkiewicz, R. L. Taylor, J.Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, Sixth Edition (2005).

O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method for Solid and Structural Mechanics, Sixth Edition (2005).

O. C. Zienkiewicz, R. L. Taylor and P. Nithiarasu, The Finite Element Method for Fluid Dynamics, Sixth Edition (2005).

T. J. R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (Paperback) (2000).

- First two are introductory, easy to follow.
- Oden, and Fish & Belytschko introductory, higher level.
- Bathe classical, but outdated. (Note: but see the 2007 edition.)
- Zienkiewicz panoramic coverage, but not approprate as introductory texts.
- Hughes: very detailed introduction, with implementation aspects.

### Wisconsin

R. D. Cook, D. S. Malkus and M. E. Plesha, Concepts and Applications of Finite Element Analysis,

### Cambridge

Huebner.

### Princeton

- T. J. R. Hughes
- Carey and Oden
- Zienkiewicz and Taylor
- Golub and Ortega

### Rice

Textbook

G.R. Buchanan, Finite Element Analysis

Reference

T.J.R. Hughes, The Finite Element Method.