FEEC is a recent advance in the mathematics of finite element methods that employs differential complexes to construct stable numerical schemes for several important types of application problems. In this talk, FEEC is applied to flow problems including Stokes equations and Biot model. More precisely we shall use H(div) elements to obtain point-wise divergence free velocity
approximation to the Stokes equations and use H(curl) element for the Biot model. These discretization is solver-friendly in the sense that efficient multigrid solvers can be developed based on the underling exact sequence. For more general finite element discretizations, our discretization can be served as a preconditioner in the framework of Fast Auxiliary Space Preconditioning (FASP) method to speed up the simulation.