Domain decomposition for coupled Stokes and Darcy flows

A non-overlapping domain decomposition method is presented to solve a coupled Stokes–Darcy flow problem in parallel by partitioning the computational domain into multiple subdomains, upon which families of coupled local problems of lower complexity are formulated. The coupling is based on appropriate interface matching conditions. The global problem is reduced to an interface problem by eliminating the interior subdomain variables. The interface problem is solved by an iterative procedure, which requires solving subdomain problems at each iteration. Finite element techniques appropriate for the type of each subdomain problem are used to discretize it. The condition number of the resulting algebraic system is analyzed and numerical tests verifying the theoretical estimates are provided.