Numerical approximation with Nitscheʼs coupling of transient Stokesʼ/Darcyʼs flow problems applied to hemodynamics

We consider a time dependent coupled Stokes/Darcy flow problem and study an approximation method based on a unified finite element scheme complemented with implicit time stepping. Our finite element formulation relies on a weighing strategy in which the physical and discretization parameters are taken into account to robustly enforce interface and boundary conditions by means of the Nitsche method. We study absolute stability and convergence of the scheme, and discuss the algebraic properties of the associated discrete problem. Finally, we present numerical experiments confirming the predicted convergence behavior and algebraic properties, and report an application to the computational analysis of blood flow and plasma filtration in arteries after the implantation of a vascular graft.