Block preconditioners for saddle point linear systems arising in the FE discretization of the Navier-Stokes equations. Application to the driven cavity problem

In this thesis, we study a Constraint Preconditioner for the saddle point linear system that arises in the Finite Element discretization of the Navier-Stokes equations, using P2-P1 elements and Picard linearization. The system is solved using the GMRES method. Our focus is in finding scalable preconditioners for the (1,1)-block and for the Schur complement: we use, respectively, a Multigrid scheme with adequate flow-following smoothing and an advanced version of the BFBt preconditioner. We present results involving the lid-driven cavity problem for viscosities up to 0.001.