A finite element scheme for the numerical solution of the Navier–Stokes/Biot coupled problem

A finite element method for a monolithic quasi-Lagrangian formulation of a fluid–porous structure interaction problem with a corrected balance of stresses on the fluid–structure interface is considered. Deformations of the elastic medium are not necessarily small and are modelled using Saint Venant–Kirchhoff (SVK) constitutive relation. The stability of the method is proved in a form of energy bound for the finite element solution.