A fast Schur complement method for the spectral element discretization of the incompressible Navier-Stokes equations (Q1346513)

The incompressible Navier-Stokes equations discretized with spectral elements are considered in three dimensions. The Uzawa algorithm is applied to decouple the velocities from the pressure. Within pressure iteration, a Helmholtz equation has to be solved. By the Schur method, the equations for the interior nodes are separated from the equations at the interfaces, and fast diagonalization techniques can be applied to the interior variables. Several ways to deal with the resulting interface problems are discussed. Finally, a comparison is made with a more classical method.