A Robin-Type Domain Decomposition Method for a Novel Mixed-Type DG Method for the Coupled Stokes--Darcy Problem

In this paper, we first propose and analyze a novel mixed-type DG method for the coupled Stokes--Darcy problem on simplicial meshes. The proposed formulation is locally conservative. A in conjunction with stress-velocity employed Stokes equations, where symmetry of stress strongly imposed. staggered exploited to discretize Darcy equations. As such, discrete can be easily adapted account Beavers--Joseph--Saffman interface conditions without introducing additional variables. Importantly, continuity normal velocity satisfied exactly at level. rigorous convergence analysis performed all Then devise domain decomposition via use Robin-type boundary conditions, which allows us solve subproblem sequentially low computational costs. iterative analyzed rigorously. particular, also works very small viscosity coefficient. Finally, several numerical experiments are carried out demonstrate capabilities accuracy scheme, method.