This monograph presents the concepts and methods needed for the numerical modelling by finite elements of the behavior of viscous Newtonian incompressible fluids.

After a short reminder of the governing equations and simplified models, a detailed introduction proposes the approximation techniques of these equations by finite elements for the space and time dependencies (diffusion, advection-diffusion and transport problems). A particular attention is paid to the space discretization of the Stokes equations and to the time algorithms for the direct numerical simulation of the Navier-Stokes equations. An ancillary chapter summarizes the solution methods for large sparse algebraic systems that are characteristic of finite element methods.

The clear, didactic and gradual approach offers a well-balanced content between theory and practice. This book constitutes an indispensable reference for Master or Ph. D students in mechanical engineering or in applied mathematics. Researchers and industrial professionals will also take full advantage to get acquainted with this numerical method for fluids.