Mathematical Problems in Elasticity and Homogenization (eBook)

O.A. Oleinik, A.S. Shamaev, G.A. Yosifian (Autoren)

eBook Download: EPUB

2009 | 1. Auflage
499 Seiten
Elsevier Science (Verlag)
978-0-08-087523-1 (ISBN)

Infos

This monograph is based on research undertaken by the authors during the last ten years. The main part of the work deals with homogenization problems in elasticity as well as some mathematical problems related to composite and perforated elastic materials. This study of processes in strongly non-homogeneous media brings forth a large number of purely mathematical problems which are very important for applications. Although the methods suggested deal with stationary problems, some of them can be extended to non-stationary equations. With the exception of some well-known facts from functional analysis and the theory of partial differential equations, all results in this book are given detailed mathematical proof.

It is expected that the results and methods presented in this book will promote further investigation of mathematical models for processes in composite and perforated media, heat-transfer, energy transfer by radiation, processes of diffusion and filtration in porous media, and that they will stimulate research in other problems of mathematical physics and the theory of partial differential equations.

Inhalt

Front Cover 1
Navier–Stokes Equations: Theory and Numerical Analysis 4
Copyright Page 5
Contents 8
Foreword 6
Chapter I The Steady-State Stokes Equations 12
Introduction 12
§1. Some function spaces 12
§2. Existence and uniqueness for the Stokes equations 31
§3. Discretization of the Stokes equations (I) 50
§4. Discretization of the Stokes equations (II) 76
§5. Numerical algorithms 149
§6. Slightly compressible fluids 158
Chapter II The Steady–State Navier–Stokes Equations 168
Introduction 168
§1. Existence and uniqueness theorems 168
§2. Discrete inequalities and compactness theorems 191
§3. Approximation of the stationary Navier–Stokes equations 210
§4. Bifurcation theory and non-uniqueness results 234
Chapter III The Evolution Navier–Stokes Equations 258
Introduction 258
§1. The linear case 258
§2. Compactness theorems 280
§3. Existence and uniqueness theorems (n = 4). 289
§4. Alternate proof of existence by semi-discretization 331
§5. Discretization of the Navier–Stokes equations: General stability and convergence theorems 342
§6. Discretization of the Navier–Stokes equations: Application of the general results 375
§7. Approximation of the Navier–Stokes equations by the Fractional Step Method 406
§8. Approximation of the Navier–Stokes equations by the artificial compressibility method 437
Comments 469
References 475
Appendix 491
Implementation of non-conforming linear finite elements 491

Produkt-Details

• Erscheint lt. Verlag: 15.6.2009
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Bauwesen
• ISBN-10: 0-08-087523-8 / 0080875238
• ISBN-13: 978-0-08-087523-1 / 9780080875231