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Although the numerical results suggest the optimal convergence order of thetwo-grid finite element decoupled scheme for mixed Stokes-Darcy model withBeaver-Joseph-Saffman interface condition in literatures, the numericalanalysis only get the optimal error order for porous media flow and anon-optimal error order that is half order lower than the optimal one in fluidflow. The purpose of this paper is to fill in the gap between the numericalresults and the theoretical analysis. By introducing an $H^1-$ orthogonaldecomposition of a specific vector valued space, we obtain the optimal errorestimates of the velocity and pressure in fluid flow region.

Optimal Error Estimates of A Decoupled Scheme Based on Two-Grid Finite Element for Mixed Stokes-Darcy Model