Finite elements有限元，第3版：理论、快速解法及在固体力学中的应用
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作者： Dietrich Braess 著
出 版 社：
出版时间： 2007-4-1字数：版次： 1页数： 365印刷时间： 2007/04/01开本： 大32开印次： 1纸张： 胶版纸I S B N ： 9780521705189包装： 平装内容简介
This definitive introduction to finite element methods has been thoroughly updated for a third edition which features important new 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.
目录
Preface to the Third English Edition
Preface to the First English Edition
Preface to the German Edition
Notation
Chapter 1 Introduction
1 Examples and Classification of PDE'S
2 The Maximum Principle
3 Finite Difference Methods
4 A Convergence Theory for Difference Methods
Chapter 2 Conforming Finite Elements
1 Sobolev Spaces
2 Variational Formulation of Elliptic Boundary-Value Problems of Second Order
3 The Neumann Boundary-Value Problem.A Trace Theorem
4 The Ritz-Galerkin Method and Some Finite Elements
5 Some Standard Finite Elements
6 Approximation Properties
7 Error Bounds for Elliptic Problems of Second Order
8 Computational Considerations
Chapter 3 Nonconforming and Other Methods
1 Abstract Lemmas and a Simple Boundary Approximation
2 Isoparametric Elements
3 Further Tools from Functional Analysis
4 Saddle Point Problems
……
Chapter 4 The Conjugate Gradient Method
Chapter 5 Multigrid Methods
Chapter 6 Finite Elements in Solid Mechanics
References
Index