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Introduction to the finite element method. Theory, programming and applications. (English)
Hoboken, NJ: John Wiley \& Sons (ISBN 0-471-45253-X/hbk). xiii, 343~p. EUR~42.00; \sterling~32.95; \\$~42.00 (2005).
This textbook is suitable for graduate students in engineering and also for use in a senior-level course. Some knowledge of the use of ordinary and partial differential equations to describe problems related to engineering analysis is assumed, as is a rudimentary knowledge of matrix algebra. The book is divided into twelve chapters, each being devoted to some mathematical problems, and four appendices are included to describe reference material. The author starts with an elementary example of the deflection of a tightly stretched wire under a distributed load. This example is sufficient to: (a) refresh the reader on some aspects of differential equations that will prove important for understanding approximate solutions, (b) introduce the concept of approximate solutions, and (c) actually define and illustrate the finite element method (FEM). The next chapters are devoted to linear second order ordinary differential equations, a finite element function for two dimensions, Poisson’s equation (FEM approximation, applications). One chapter is devoted to higher-order elements difficulties arising in maintaining continuity of the approximating function between elements. Chapter 9 presents a FEM program for two-dimensional boundary value problems. All codes are written in MATLAB script, which can be run on the student version of MATLAB. Also, a number of applications related to various fields of engineering is provided. In the exercises at the end of most chapters, there is a section on “Numerical experiments and code development” with problems that encourage students to test the codes. All codes, example data files, and auxiliary codes are available for download on the website for this book.
Reviewer: Pavol Chocholatý (Bratislava)