Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics

ISBN-13: 9780521705189 / Angielski / Miękka / 2007 / 384 str.

Dietrich Braess

Opis

This definitive introduction to finite element methods was thoroughly updated for this 2007 third edition, which features important material for both research and application of the finite element method. The discussion of saddle-point problems is a highlight of the book and has been elaborated to include many more nonstandard applications. The chapter on applications in elasticity now contains a complete discussion of locking phenomena. The numerical solution of elliptic partial differential equations is an important application of finite elements and the author discusses this subject comprehensively. These equations are treated as variational problems for which the Sobolev spaces are the right framework. Graduate students who do not necessarily have any particular background in differential equations, but require an introduction to finite element methods will find this text invaluable. Specifically, the chapter on finite elements in solid mechanics provides a bridge between mathematics and engineering.

Recenzje

'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

Spis treści

Preface to the third English edition; Preface to the first English edition; Preface to the German edition; Notation; 1. Introduction; 2. Conforming finite elements; 3. Nonconforming and other methods; 4. The conjugate gradient method; 5. Multigrid methods; 6. Finite elements in solid mechanics; References; Index.