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Finite element analysis and applications. (English) Zbl 0577.65093
A Wiley-Intersience Publication. Chichester etc.: John Wiley & Sons. XII, 260 p. £10.95 (1985).
This book is a substantially revised and updated version of an earlier one by the authors [The finite element method in partial differential equations (1977; Zbl 0344.35001)]. In the preface to the 1977 version, the authors state that the text ”is aimed at final-year undergraduate and first-year postgraduate students in mathematics and engineering.” The current version is aimed at ”students in mathematical sciences or engineering”. The difference between the two statements reflects a difference in orientation of the texts. The current version is directed more toward applications than theory, with many worked examples including plots and tables of results. The authors summarize the underlying theory primarily in order to promote intelligent use of the finite element method. The years between 1977 and 1985 have seen enormous advances in both theory and application of finite element methods. The differences between this book and its predecessor reflect those changes. The chapters have been reorganized and many of the sections rewritten. The two most noticeable changes are in Chapter 4, Methods of approximation, which now occupies almost seventy pages, and in Chapter 7, Developments and applications, which is over thirty-five pages long. In the earlier volume the chapter entitled Methods of approximation is only thirty-five pages long and the chapter entitled Developments and applications discusses such topics as non-conforming elements and blending functions which have now been placed elsewhere. As the title suggests, the authors have chosen to concentrate entirely on finite element methods. No reference is made to the theory of finite difference methods even when the two are closely related, such as upwinding for fluid-flow and alternating-direction solution methods. The dismissal of iterative solution methods as suitable for equations derived from finite differences but not finite elements ignores a large and successful body of literature. The authors have kept the reference list short. They include only those works which are actually referenced in the text. This approach can lead to a somewhat unbalanced view of the subject in that only seven out of over 220 citations were written before 1961. Such theorems as the lemma of Lax and Milgram are stated and named, but reference is made to standard texts rather than the original papers. The authors have taken the trouble to update some references in their earlier volume to more generally available papers rather than research reports.
Reviewer: M.Sussman

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74S05 Finite element methods applied to problems in solid mechanics
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
76M99 Basic methods in fluid mechanics
00A06 Mathematics for nonmathematicians (engineering, social sciences, etc.)