Numerical analysis of the coupling of free fluid with a poroelastic material

This paper presents a numerical solution of the coupled system of the time-dependent Stokes and fully dynamic Biot equations. The numerical scheme is based on standard inf-sup stable finite elements in space and the Backward Euler scheme in time. We establish stability of the scheme and derive error estimates for the fully discrete coupled scheme. To handle realistic parameters which may cause nonphysical oscillations in the pore fluid pressure, a heuristic stabilization technique is considered. Numerical errors and convergence rates for smooth problems as well as tests on realistic material parameters are presented.