Mathematics and Finite Element Discretizations of Incompressible Navier–Stokes Flows: Revised and Expanded Edition

In this revised and expanded edition of Girault and Raviart’s 1986 textbook Finite Element Methods for Navier–Stokes Equations (Springer-Verlag), readers will find rigorous proof of stability and convergence, analysis of practical algorithms, and a stand-alone chapter on finite element methods that is applicable to a large range of PDEs. In addition to the basic theoretical analysis, this book covers up-to-date finite element discretizations of incompressible Navier–Stokes equations; a variety of numerical algorithms used in the computer implementation of Navier–Stokes equations and numerical experiments; standard and nonstandard boundary conditions and their numerical discretizations via the finite element methods; and conforming and nonconforming finite elements, as well as their stability and instability.

This book is intended for applied mathematicians and graduate students interested in learning about the theory of various finite element methods for solving the Navier–Stokes equations. Engineers seeking reliable algorithms for computational fluid dynamics will also find the book of interest.