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We study a finite element computational model for solving the coupled problemarising in the interaction between a free fluid and a fluid in a poroelasticmedium. The free fluid is governed by the Stokes equations, while the flow inthe poroelastic medium is modeled using the Biot poroelasticity system.Equilibrium and kinematic conditions are imposed on the interface. A mixedDarcy formulation is employed, resulting in continuity of flux condition ofessential type. A Lagrange multiplier method is employed to impose weakly thiscondition. A stability and error analysis is performed for the semi-discretecontinuous-in-time and the fully discrete formulations. A series of numericalexperiments is presented to confirm the theoretical convergence rates and tostudy the applicability of the method to modeling physical phenomena and thesensitivity of the model with respect to its parameters.

A Lagrange multiplier method for a Stokes-Biot fluid-poroelastic structure interaction model