Finite Elements

'This is a well written book on the mathematical foundation of the finite element method which should appeal to graduate mathematicians and researchers in numerical methods and theoretical mechanics. The coverage of the mathematical theories used in the finite element formulation is comprehensive.' A. A. Becker, Journal of Mechanical Engineering Science '... an excellent book on the subject, with respect to contents, readability as well as presentation ... highly recommended.' Michael Schafer, Zentralblatt fur Mathematik '... has advanced to be one of the most commonly used textbooks in this area.' Monatshefte fur Mathematik 'Carefully written and remarkably error-free, Braess's book introduces partial differential equations (PDEs) and methods used to solve them numerically. It introduces PDEs and their classification, covers (briefly) finite-difference methods, and then offers a thorough treatment of finite-element methods, both conforming and nonconforming. After discussing the conjugate gradient method and multigrid methods, Braess concludes with a chapter on finite elements in solid mechanics. The book is written from a theoretical standpoint, and the standard convergence theorems and error estimates are provided and proved. Although a background in differential equations, analysis, and linear algebra is not necessary to read the book, it would be helpful. The level is that of a graduate course in a mathematics department. Practical considerations for coding the various methods are only occasionally discussed. There are exercises at the end of each section varying from two to six problems, about two-thirds of them theoretical in nature. The book can be used as a resource. Extensive and valuable bibliography. Recommended for graduate students.' J. H. Ellison, Grove City College