A multipoint stress-flux mixed finite element method for the Stokes-Biot model

In this paper we present and analyze a fully-mixed formulation for the coupled problem arising in interaction between free fluid poroelastic medium. The flows regions are governed by Stokes Biot equations, respectively, transmission conditions given mass conservation, balance of stresses, Beavers-Joseph-Saffman law. We apply dual-mixed formulations both domains, where symmetry stress tensors is imposed setting vorticity structure rotation as auxiliary unknowns. turn, since become essential, they weakly introducing traces velocity, media pressure on interface associated Lagrange multipliers. existence uniqueness solution established continuous weak formulation, well semidiscrete continuous-in-time with non-matching grids, together corresponding stability bounds. addition, develop new multipoint stress-flux mixed finite element method involving vertex quadrature rule, which allows local elimination rotations, Darcy fluxes. Well-posedness error analysis rates convergence fully-discrete scheme complemented several numerical experiments.