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Author: Vivette Girault Publisher: Springer Science & Business Media ISBN: 3642616232 Category : Mathematics Languages : en Pages : 386
Book Description
The material covered by this book has been taught by one of the authors in a post-graduate course on Numerical Analysis at the University Pierre et Marie Curie of Paris. It is an extended version of a previous text (cf. Girault & Raviart [32J) published in 1979 by Springer-Verlag in its series: Lecture Notes in Mathematics. In the last decade, many engineers and mathematicians have concentrated their efforts on the finite element solution of the Navier-Stokes equations for incompressible flows. The purpose of this book is to provide a fairly comprehen sive treatment of the most recent developments in that field. To stay within reasonable bounds, we have restricted ourselves to the case of stationary prob lems although the time-dependent problems are of fundamental importance. This topic is currently evolving rapidly and we feel that it deserves to be covered by another specialized monograph. We have tried, to the best of our ability, to present a fairly exhaustive treatment of the finite element methods for inner flows. On the other hand however, we have entirely left out the subject of exterior problems which involve radically different techniques, both from a theoretical and from a practical point of view. Also, we have neither discussed the implemen tation of the finite element methods presented by this book, nor given any explicit numerical result. This field is extensively covered by Peyret & Taylor [64J and Thomasset [82].
Author: Vivette Girault Publisher: Springer Science & Business Media ISBN: 3642616232 Category : Mathematics Languages : en Pages : 386
Book Description
The material covered by this book has been taught by one of the authors in a post-graduate course on Numerical Analysis at the University Pierre et Marie Curie of Paris. It is an extended version of a previous text (cf. Girault & Raviart [32J) published in 1979 by Springer-Verlag in its series: Lecture Notes in Mathematics. In the last decade, many engineers and mathematicians have concentrated their efforts on the finite element solution of the Navier-Stokes equations for incompressible flows. The purpose of this book is to provide a fairly comprehen sive treatment of the most recent developments in that field. To stay within reasonable bounds, we have restricted ourselves to the case of stationary prob lems although the time-dependent problems are of fundamental importance. This topic is currently evolving rapidly and we feel that it deserves to be covered by another specialized monograph. We have tried, to the best of our ability, to present a fairly exhaustive treatment of the finite element methods for inner flows. On the other hand however, we have entirely left out the subject of exterior problems which involve radically different techniques, both from a theoretical and from a practical point of view. Also, we have neither discussed the implemen tation of the finite element methods presented by this book, nor given any explicit numerical result. This field is extensively covered by Peyret & Taylor [64J and Thomasset [82].
Author: Roger Temam Publisher: American Mathematical Society ISBN: 1470477866 Category : Mathematics Languages : en Pages : 426
Book Description
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.
Author: Hans-Görg Roos Publisher: Springer Science & Business Media ISBN: 3662032066 Category : Mathematics Languages : en Pages : 364
Book Description
The analysis of singular perturbed differential equations began early in this century, when approximate solutions were constructed from asymptotic ex pansions. (Preliminary attempts appear in the nineteenth century [vD94].) This technique has flourished since the mid-1960s. Its principal ideas and methods are described in several textbooks. Nevertheless, asymptotic ex pansions may be impossible to construct or may fail to simplify the given problem; then numerical approximations are often the only option. The systematic study of numerical methods for singular perturbation problems started somewhat later - in the 1970s. While the research frontier has been steadily pushed back, the exposition of new developments in the analysis of numerical methods has been neglected. Perhaps the only example of a textbook that concentrates on this analysis is [DMS80], which collects various results for ordinary differential equations, but many methods and techniques that are relevant today (especially for partial differential equa tions) were developed after 1980.Thus contemporary researchers must comb the literature to acquaint themselves with earlier work. Our purposes in writing this introductory book are twofold. First, we aim to present a structured account of recent ideas in the numerical analysis of singularly perturbed differential equations. Second, this important area has many open problems and we hope that our book will stimulate further investigations.Our choice of topics is inevitably personal and reflects our own main interests.
Author: F. Thomasset Publisher: Springer Science & Business Media ISBN: 3642870473 Category : Science Languages : en Pages : 168
Book Description
In structure mechanics analysis, finite element methods are now well estab lished and well documented techniques; their advantage lies in a higher flexibility, in particular for: (i) The representation of arbitrary complicated boundaries; (ii) Systematic rules for the developments of stable numerical schemes ap proximating mathematically wellposed problems, with various types of boundary conditions. On the other hand, compared to finite difference methods, this flexibility is paid by: an increased programming complexity; additional storage require ment. The application of finite element methods to fluid mechanics has been lagging behind and is relatively recent for several types of reasons: (i) Historical reasons: the early methods were invented by engineers for the analysis of torsion, flexion deformation of bearns, plates, shells, etc ... (see the historics in Strang and Fix (1972) or Zienckiewicz (1977». (ii) Technical reasons: fluid flow problems present specific difficulties: strong gradients,l of the velocity or temperature for instance, may occur which a finite mesh is unable to properly represent; a remedy lies in the various upwind finite element schemes which recently turned up, and which are reviewed in chapter 2 (yet their effect is just as controversial as in finite differences). Next, waves can propagate (e.g. in ocean dynamics with shallowwaters equations) which will be falsely distorted by a finite non regular mesh, as Kreiss (1979) pointed out. We are concerned in this course with the approximation of incompressible, viscous, Newtonian fluids, i.e. governed by N avier Stokes equations.
Author: P.G. Ciarlet Publisher: Elsevier ISBN: 0080875254 Category : Mathematics Languages : en Pages : 551
Book Description
The objective of this book is to analyze within reasonable limits (it is not a treatise) the basic mathematical aspects of the finite element method. The book should also serve as an introduction to current research on this subject. On the one hand, it is also intended to be a working textbook for advanced courses in Numerical Analysis, as typically taught in graduate courses in American and French universities. For example, it is the author's experience that a one-semester course (on a three-hour per week basis) can be taught from Chapters 1, 2 and 3 (with the exception of Section 3.3), while another one-semester course can be taught from Chapters 4 and 6. On the other hand, it is hoped that this book will prove to be useful for researchers interested in advanced aspects of the numerical analysis of the finite element method. In this respect, Section 3.3, Chapters 5, 7 and 8, and the sections on "Additional Bibliography and Comments should provide many suggestions for conducting seminars.
Author: Philippe G. Ciarlet Publisher: SIAM ISBN: 0898715148 Category : Mathematics Languages : en Pages : 552
Book Description
This is the only book available that fully analyzes the mathematical foundations of the finite element method. Not only is it valuable reference and introduction to current research, it is also a working textbook for graduate courses in numerical analysis, including useful figures and exercises of varying difficulty.
Author: Hans-Görg Roos Publisher: Springer Science & Business Media ISBN: 3540344675 Category : Mathematics Languages : en Pages : 599
Book Description
This new edition incorporates new developments in numerical methods for singularly perturbed differential equations, focusing on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics.
Author: Vivette Girault
Author: Vivette Girault
Author: Roger Temam
Author: C. Cuvelier
Author: Hans-Görg Roos
Author: F. Thomasset
Author: P.G. Ciarlet
Author: 
Author: Philippe G. Ciarlet
Author: Hans-Görg Roos
Author: H. Cabannes