# Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics 有限元：在

Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics 有限元：在固体力学中的理论、快速解决和应用

I S B N ： 0521705185

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.

Preface to the Third English Edition

Preface to the First English Edition

Preface to the German Edition

Notation

Chapter I　Introduction

1. Examples and Classification of PDE's

2. The Maximum Principle

3. Finite Difference Methods

4. A Convergence Theory for Difference Methods

Chapter II　Conforming Finite Elements

1. Sobolev Spaces

2. Variational Formulation of Elliptic Boundary-Value Problems of

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 III　Nonconforming and Other Methods

1. Abstract Lemmas and a Simple Boundary Approximation

2. Isoparametric Elements

3. Further Tools from Functional Analysis

……

Chapter IV The Conjugate Gradient Method

Chapter V Multigrid Methods

Chapter VI Finite Elements in Solind Mechanics

References

Index

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