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

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. The reader will find in this reference further mathematical material.