A monolithic fluid-porous structure interaction finite element method

Abstract: The paper introduces a fully discrete quasi-Lagrangian finite element method for a monolithic formulation of a fluid-porous structure interaction problem. The method is second order in time and allows a standard $P_2-P_1$ (Taylor--Hood) finite element spaces for fluid problems in both fluid and porous domains. The performance of the method is illustrated on a series of numerical experiments.