This comprehensive two volume reference work is devoted to theimportant details regarding the application of the finite elementmethod to incompressible flows, addressing the theoreticalbackground and the detailed development of appropriate numericalmethods applied to their solution. Volume One provides extensivecoverage of the prototypical fluid mechanics equation: theadvection-diffusion equation. In addition, for both this equationand the equations of principal interest - the Navier-Stokesequations - (covered in detail in Volume Two), a discussion of boththe continuous and discrete equations is presented. Also addressedare explanations of how to properly march the time-dependentequations using smart implicit methods. Boundary and initialconditions, so important in applications, are thoroughly describedand discussed, including well-posedness. The important role playedby the pressure, so confusing in the past, is carefully explained.Together, this two volume work explains and emphasizes consistencyin six areas: * consistent mass matrix * consistent pressure Poisson equation * consistent penalty methods * consistent normal direction * consistent heat flux * consistent forces Fully indexed and referenced, these two volumes form an essentialreference tool for all research students and applied scientists inincompressible fluid mechanics.weiterlesen