FIRST-ORDER SYSTEM LEAST SQUARES FOR COUPLED STOKES-DARCY FLOW

The coupled problem with Stokes flow in one subdomain and a Darcy flow model in a second subdomain is studied in this paper. Both flow problems are treated as first-order systems, involving pseudostress and velocity in the Stokes case and using a flux-pressure formulation in the Darcy subdomain as process variables, respectively. The Beavers-Joseph-Saffman interface conditions are treated by an appropriate interface functional which is added to the least squares functional associated with the subdomain problems. A combination of H(div)-conforming Raviart-Thomas and standard H(1)-conforming elements is used for the Stokes as well as for the Darcy subsystem. The homogeneous least squares functional is shown to be equivalent to an appropriate norm allowing the use of standard finite element approximation estimates. It also establishes the fact that the local evaluation of the least squares functional itself constitutes an a posteriori error estimator to be used for adaptive refinement strategies.