Abstract
In this paper, we investigate a mortar element method for the time dependent coupling of incompressible flow and porous media flow which are governed by non-stationary Stokes and Darcy equations, respectively. The interface conditions are given by mass conservation, the balance of the normal forces and the Beavers–Joseph–Saffman law. We consider the dual-mixed formulation in Darcy region where velocity and pressure are both unknowns. We employ the lowest order Raviart–Thomas element for Darcy flow and choose Bernardi–Raugel element in the free fluid region. The backward Euler scheme is adopt to yield the fully discrete algorithm. At each single time step, we present a priori error estimate which shows the linear convergence. At the final, numerical experiments are provided to illustrate the performance of the developed algorithm that verify our analysis.
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