A mixed elasticity formulation for fluid–poroelastic structure interaction

We develop a mixed finite element method for the coupled problem arising in interaction between free fluid governed by Stokes equations and flow deformable porous medium modeled Biot system of poroelasticity. Mass conservation, balance stress, Beavers–Joseph–Saffman condition are imposed on interface. consider fully formulation based weakly symmetric stress-displacement-rotation elasticity Darcy velocity-pressure formulation. A is used equations. The interface conditions incorporated through introduction traces structure velocity pressure as Lagrange multipliers. Existence uniqueness solution established continuous weak Stability error estimates derived semi-discrete continuous-in-time approximation. Numerical experiments presented to verify theoretical results illustrate robustness with respect physical parameters.