This book offers a complete introduction on the application of the finite element method to fluid mechanics. The book begins with a useful summary of all relevant partial differential equations before moving on to discuss convection stabilization procedures, steady and transient state equations, and numerical solution of fluid dynamic equations. This expanded eighth edition starts by explaining the character-based split (CBS) scheme before exploring a range of other methods including SUPG/PSPG, space-time, and VMS methods. There are also new chapters on topics such as: Data-driven computational fluid dynamics, Buoyancy Driven Flows. and High-order Methods.