Domain decomposition method for the fully-mixed Stokes–Darcy coupled problem

In this paper, a parallel domain decomposition method is proposed, for solving the fully-mixed Stokes–Darcy coupled problem with the Beavers–Joseph–Saffman (BJS) interface conditions. With newly constructed Robin-type boundary conditions, the present method adopts modified weak formulation to decouple the original problem into two independent subproblems. The equivalence between the original problem and the decoupled subproblems is derived under some compatibility conditions. Another equivalence of two weak formulations with different spaces is also established, for subsequent convergence analysis based on the decoupled modified weak formulation. Moreover, the convergence of the iterative parallel method in a more general framework is shown. With some suitable choice of parameters, both mesh-dependent and mesh-independent convergence rates are proved rigorously. Finally, we present several numerical examples to show the exclusive features of the proposed method.