FEM-MsFEM hybrid method for the Stokes-Darcy model

This paper explores the application of hybrid of the finite element method and multiscale finite element method (FEM-MsFEM) to address the steady-state Stokes-Darcy problems with Beavers-Joseph-Saffman (BJS) interface conditions in highly heterogeneous porous media. We propose an algorithm for this multiscale Stokes-Darcy model. The FEM-MsFEM hybrid method adapts to the characteristics of different regions. MsFEM basis functions are applied to the Darcy region, whereas standard finite element basis functions are utilized for the Stokes region. Afterward, the FEM-MsFEM basis functions are used for computations with the Robin-Robin domain decomposition algorithm. Furthermore, this special domain decomposition algorithm preserves a convergence rate independent of the mesh size. Subsequently, we conduct error analysis based on $L^2$ and $H^1$ norms for this FEM-MsFEM hybrid method. Finally, we present extensive numerical tests, illustrating the results of error and convergence analysis.