Analysis of a stabilized finite element method for fluid flows through a porous interface

This work is devoted to the numerical simulation of an incompressible fluid through a porous interface, modeled as a macroscopic resistive interface term in the Stokes equations. We improve the results reported in M.A. Fernández, J.-F. Gerbeau, V. Martin, Numerical simulation of blood flows through a porous interface, Math. Model. Num. Anal. (M2AN) 42 (6) (2008) 961–990], by showing that the standard Pressure Stabilized Petrov–Galerkin (PSPG) finite element method is stable, and optimally convergent, without the need for controlling the pressure jump across the interface.