Finite Element Approximation of the Navier-Stokes Equations
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749 V. Girault P.-A. Raviart
Finite Element Approximation of the Navier-Stokes Equations Revised Reprint of the First Edition
Springer-Verlag Berlin Heidelberg New York 1981
Authors Vivette Girault Pierre-Arnaud Raviart Analyse Numerique Tour 55-65, 5eme etage Universite Pierre et Marie Curie 4, Place Jussieu F-75230 Paris Cedex 05
AMS Subject Classifications (1970) : 35010, 65-06, 65 M XX, 65M15, 65 N30, 76-XX ISBN 3-540-09557-8 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-09557-8 Springer-Verlag NewYork Heidelberg Berlin Library of Congress Cataloging in Publication Data Girault, Vivette,1943Finite element approximation of the Navier-Stokes equations . (Lecture notes in mathematics ; 749) Bibliography: p. Includes index. 1 . Viscous flow. 2 . Navier-Stokes equations-- Numerical solutions . 3. Finite element method. I . Raviart, P . A.,1939-- joint author. II . Title. III . Series: Lecture notes in mathematics (Berlin) ; 749 . 0A3.L28 no. 749 [0A929] 510' .8s [519 .4] 79-21917 ISBN 0-387-09557-8
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INTRODUCTION
The contents of this publication have been taught at the University Pierre & 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 [44
1.
The reader will find in this reference further mathematical
material . Besides R . Temam, the authors are gratefully indebted to M . Crouzeix for many helpful discussions and for providing original proofs of a number of theorems .
CONTENTS
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