A Stabilized Finite Volume Element Method for Stationary Stokes–Darcy Equations Using the Lowest Order

We present a stabilized finite volume element method for the coupled Stokes–Darcy problem with the lowest order [Formula: see text] element for the Stokes region and [Formula: see text] element for the Darcy region. Based on adding a jump term of discrete pressure to the approximation equation, a discrete inf-sup condition is established for the proposed method. The optimal error estimates in the [Formula: see text]-norm for the velocity and piezometric head and in the [Formula: see text]-norm for the pressure are proved. And they are also verified through some numerical experiments. Two figures are given to show the full comparison for the local mass conservation between the proposed method and the stabilized finite element method. And this method can also be computed directly in the irregular domain according to the last experiment.