Natural finite element techniques for viscous fluid motion

A survey on modern developments in finite element methods for fluid motion is given, stressing a natural description of the relevant phenomena and emphasizing incompressible media. Natural terminology is introduced and methodically applied to the formulation of field quantities characteristic of fluid motion. The transition to finite domains as a foundation for the development of the finite element theory of the flow problem is addressed. The flow problem is discretized with respect to the space variables and is integrated in the time domain. Approximate numerical schemes for this purpose are reviewed and solution strategies for the resulting algebraic equations governing flow phenomena are discussed. The effective numerical treatment of the governing finite element equations is addressed taking into account recent developments in iterative solution techniques for large systems of equations. Finally, some typical examples of viscous fluid motion are numerically analyzed.