A posteriori error estimate for the H(div) conforming mixed finite element for the coupled Darcy-Stokes system

An H(div) conforming mixed finite element method has been proposed for the coupled Darcy-Stokes flow in Kanschat and Rivière (2010) [12], which imposes normal continuity on the velocity field strongly across the Darcy-Stokes interface. Here, we develop an a posteriori error estimator for this H(div) conforming mixed method, and prove its global reliability and efficiency. Due to the strong coupling on the interface, special techniques need to be employed in the proof. This is the main difference between this paper and Babuška and Gatica's (2010) work [38], in which they analyzed an a posteriori error estimator for the mixed formulation using weakly coupled interface conditions.