The finite-element method was originally developed by engineers in the 1950s to analyze large structural systems for aircraft. Aimed at advanced level undergraduates of engineering and fluid mechanics and researchers, engineers and scientists in fluid mechanics, mechanical and chemical engineering, this text derives, develops and applies finite-element solution methodology directly to the differential equation systems governing distinct and practical problem classes in fluid mechanics. It is principally a text on fluid mechanics and the theory of its computational simulation, for those with a basic interest in fluid mechanics.