Finite element methods for the viscous incompressible fluid

We consider the numerical implementations of the standard one-level finite element method and two-level finite element method for the steady and the unsteady Navier–Stokes equations, respectively. Two numerical examples are presented: first, we solve the steady Navier–Stokes equations in a bounded multiple connected domain by the standard one-level finite element method, while we calculate the unsteady Navier–Stokes equations by full discrete two-level finite element method. The numerical results show that the two methods are feasible, and the new two-level finite element method is significantly effective.