Finite element methods for the fluids. (Méthodes des éléments finis pour les fluides.) (French) Zbl 0748.76003

Recherches en Mathématiques Appliquées. 7. Paris etc.: Masson. 199 p. (1988).
This book provides a nice exposition of a mathematical introduction (at graduate level) to the finite element methods applied to problems of fluid mechanics. In the first chapter there is a discussion of the main equations of fluid mechanics and their derivation. The second chapter deals with a potential correction method for weakly irrotational flows. In the third chapter the methods of upwinding and artificial viscosity are applied to convection-diffusion problems. A finite elements treatment of the generalized Stokes problem is done in the fourth chapter. The methods developed in the last two chapters are applied to the Navier- Stokes equations in the fifth chapter. Finally, in the sixth chapter the compressible Euler equations are considered. The book ends with an appendix describing a computer program (written by the author) which solves some of the problems of the book.


76-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to fluid mechanics
76M10 Finite element methods applied to problems in fluid mechanics
76Dxx Incompressible viscous fluids
76Bxx Incompressible inviscid fluids
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76Rxx Diffusion and convection