Solution algorithms for incompressible viscous flows at high Reynolds numbers (Q1281206)

The author considers the problem of finite element approximation of incompressible Navier-Stokes equations in two- or three-dimensional polyhedral domains. It is known that most of the algorithms become unstable when the Reynolds numbers are high, i.e. \(0<\text{Re}\leq O(h)\) (\(h\) is a global size of the finite element mesh). Here the author presents an analysis of some new methods of solution for high Reynolds numbers (multi-level Newton method with artificial viscosity).