The Navier–Stokes Equations

The Navier–Stokes equations model flows of incompressible viscous fluids. Such flows arise in virtually all fields of science and engineering, either on their own or as part of more complex multi-physics phenomena. This makes the Navier–Stokes equations one of the most important modeling tools in science and engineering, and their numerical solutions one of the most important tasks in computational science.

Our interest in considering the Navier–Stokes equations is motivated not only by their intrinsic importance, but also to provide a setting for discussing how leastsquares finite element methods (LSFEMs) can be applied to nonlinear problems. As such, this chapter provides useful insights on how LSFEMs can be used for other nonlinear partial differential equations (PDEs).