Navier-Stokes equations : theory and numerical analysis / by Roger Temam.

Format:

Book

Author/Creator:

Temam, Roger, author.

Series:

AMS Chelsea Publishing Series

AMS Chelsea Publishing, v. 343

Language:

English

Subjects (All):

Navier-Stokes equations.

Physical Description:

1 online resource (411 pages)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : AMS Chelsea Publishing, 2001.

Summary:

Originally published in 1977, the book is devoted to the theory and numerical analysis of the Navier-Stokes equations for viscous incompressible fluid. On the theoretical side, results related to the existence, the uniqueness, and, in some cases, the regularity of solutions are presented. On the numerical side, various approaches to the approximation of Navier-Stokes problems by discretization are considered, such as the finite dereference method, the finite element method, and the fractional steps method. The problems of stability and convergence for numerical methods are treated as completely as possible.The new material in the present book (as compared to the preceding 1984 edition) is an appendix reproducing a survey article written in 1998. This appendix touches upon a few aspects not addressed in the earlier editions, in particular a short derivation of the Navier-Stokes equations from the basic conservation principles in continuum mechanics, further historical perspectives, and indications on new developments in the area. The appendix also surveys some aspects of the related Euler equations and the compressible Navier-Stokes equations.The book is written in the style of a textbook and the author has attempted to make the treatment self-contained. It can be used as a textbook or a reference book for researchers. Prerequisites for reading the book include some familiarity with the Navier-Stokes equations and some knowledge of functional analysis and Sololev spaces.

Contents:

Intro

Contents

Preface to the AMS Chelsea edition

Preface to the third (revised) edition

Foreword

CHAPTER 1 The Steady-State Stokes Equations

1. Some function spaces

2. Existence and uniqueness for the Stokes equations

3. Discretization of the Stokes equations (I)

4. Discretization of Stokes equations (II)

5. Numerical algorithms

6. The penalty method

CHAPTER 2 Steady-State Navier-Stokes Equations

1. Existence and uniqueness theorems

2. Discrete inequalities and compactness theorems

3. Approximation of the stationary Navier-Stokes equations

4. Bifurcation theory and non-uniqueness results

CHAPTER 3 The Evolution Navier-Stokes Equation

1. The linear case

2. Compactness theorems

3. Existence and uniqueness theorems (n ≤ 4)

4. Alternate proof of existence by semi-discretization

5. Discretization of the Navier-Stokes equations: General stability and convergence theorems

6. Discretization of the Navier-Stokes equations: Application of the general results

7. Approximation of the Navier-Stokes equations by the projection method

8. Approximation of the Navier-Stokes equations by the artificial compressibility method

APPENDIX I Properties of the Curl Operator and Application to the Steady-State Navier-Stokes Equations

1. Functional properties of the curl operator

2. Application to the non-homogeneous steady-state Navier-Stokes equations

APPENDIX II Implementation of Non-conforming inear Finite Elements (Approximation APX5-Two-dimensional Case)

0. Test problems

1. The triangulation

2. The nodes

3. Computation of the basis function on a given triangle

4. Solution of the Stokes problem

5. Solution of Navier-Stokes equations

APPENDIX III Some Developments on Navier-Stokes Equations in the Second Half of the 20th Century.

Part I: The incompressible Navier-Stokes equations

1. Existence, uniqueness and regularity of solutions

2. Attractors and turbulence

Part II: Other problems, other equations

3. Compressible and inviscid flows

4. Some other problems and equations

Bibliography to Appendix III

Comments

Chapter 1

Chapter 2

Chapter 3

Additional comments to the third (revised) edition

Bibliography

Index

About this book.

Notes:

"Third (revised) edition"--P. xi.

Originally published: Amsterdam ; New York : North-Holland, 1977. With new introd.

Includes bibliographical references and index.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

1-4704-2994-2

OCLC:

982012520