Pressure projection stabilizations for Galerkin approximations of Stokes' and Darcy's problem

In this study, we consider some recent stabilization techniques for the Stokes' problem and show that they are instances of the framework proposed by Brezzi and Fortin in “A minimal stabilisation procedure for mixed finite element methods” (Numer Math 89, (2001) 457). We also propose an analysis for Taylor‐Hood elements with discontinuous pressures stabilized using penalization of the interelement pressure jumps.