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].

Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms (SPRINGER SERIES IN COMPUTATIONAL MATHEMATICS)

Science & Math

Girault, Vivette

Raviart, Pierre-Arnaud

Mathematics

Springer, Verlag

<p>The contents of this publication have been taught at the University Pierre &amp; Marie Curie as a graduate course in numerical analysis during the academic year 1977-78. In the last few years, many engineers and mathematicians have concentrated their efforts on the numerical solution of the Navier-Stokes equations by finite element methods. The purpose of this series of lectures is to provide a fairly comprehensive treatment of the most recent mathematical developments in that field. It is not intended to give an exhaustive treatment of all finite element methods available for solving the Navier-Stokes equations. But instead, it places a great emphasis on the finite element methods of mixed type which play a fundamental part nowadays in numerical hydrodynamics. Consequently, these lecture notes can also be viewed as an introduction to the mixed finite element theory .We have tried as much as possible to make this text self-contained. In this respect, we have recalled a number of theoretical results on the pure mathematical aspect of the Navier-Stokes problem and we have frequently referred to the recent book by R. Temam. The reader will find in this reference further mathematical material.</p>

Finite Element Approximation of the Navier-Stokes Equations (Lecture Notes in Mathematics, 749)

Springer

<p>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 &amp; 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 &amp; Taylor [64J and Thomasset [82].</p>

Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms (Springer Series in Computational Mathematics)

Computers & Technology

Computer Science

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