Summary: In this work we perform an experimental study of iterative methods for solving large sparse linear systems arising from a second-order 2D mimetic discretization. The model problem is the 2D Poisson equation with different boundary conditions. We use GMRES with the restarted parameter and BiCGstab as iterative methods. We also use various preconditioning techniques including the robust preconditioner ILUt. The numerical experiments consist of large sparse linear systems with up to 643 200 degrees of freedom.