The numerical solution of coupled Darcy-Stokes flow problem is studied in this paper. The coupled Darcy-Stokes flow models are composed by Stokes equation in the flow domain and by Darcy's law in porous medium domain, and by proper interface conditions between the two domains. By introduced Lagrange multipliers to process interface, New variational form for coupled Darcy-Stokes model is proposed. The problem is discreted by the low order conforming H(div) R-T elements . Lastly, we prove the existence and uniqueness of the discrete problem and get error estimates.
