Finite elements. Theory, fast solvers, and applications in solid mechanics. Transl. from the German by Larry L. Schumaker. 2nd ed. (English) Zbl 0976.65099

Cambridge: Cambridge University Press. xvii, 352 p. (2001).
For reviews of the original German edition (Springer 1992), the second German edition (Springer 1997) and the first English edition (Cambridge Univ. press 1997) see Zbl 0754.65084, Zbl 0870.65097 and Zbl 0894.65054.
As the former editions the present text can be considered as an excellent book on the subject, with respect to contents, readability as well as presentation. The mathematical theory of finite elements and the related topics covered (e.g. cg-methods, multigrid methods, solid mechanics) is presented in a rigorous and very systematic way. Compared to the first edition the general structure of the text has not changed, but the present second edition contains some new material related to actual research and applications of the finite element method, which further improved the quality of the presentation. In particular, for readers interested in the mathematical background of the subject (mathematicians as well as engineers) the book is highly recommended.


65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
74S05 Finite element methods applied to problems in solid mechanics
35J25 Boundary value problems for second-order elliptic equations
65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
74B05 Classical linear elasticity
74K20 Plates
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems