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Finite elements. Computational aspects. (English) Zbl 0558.73064
The Texas Finite Element Series, Vol. III. Englewood Cliffs, New Jersey: Prentice-Hall, Inc. X. 350 p. $ 44.50 (1984).
This book, volume three of a series of six publications entitled The Texas Finite Element Series [for Vol. I (1981) see Zbl 0459.65070, for Vol. II (1983) see Zbl 0515.65075], discusses the computational aspects of finite element computer programs for various applications in engineering. Basically, the book requires the initial reading of volume one of the series and extends the range of numerical implementations to a wide degree of sophistication, compatible with the current state of the art of the finite element technique.
Chapter one presents an overview of the general structure of FE-programs, including pre- and post-processors. This is followed by the important subject of mesh generation and mesh refinement described in chapter two. In addition, this chapter also presents and discusses the existing refinement criteria based on error estimate procedures, leading to hierarchic elements. The solution of systems of linear equations is the subject of chapter three where an update view of the different techniques is presented. Chapter four discusses eigenvalue problems in a sufficiently thorough manner and chapter five includes time dependent problems, both as an extension of the formulations presented previously.
Throughout the text specific algorithms that illustrate the numerical procedures are presented in an ALGOL-like pseudo-language which do not require further description. The book is recommended to those in search of an up to date view on the subject and also provides a good list of references for further reading.
Reviewer: J.C.F.Telles

MSC:
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
74S99 Numerical and other methods in solid mechanics
74-04 Software, source code, etc. for problems pertaining to mechanics of deformable solids