Error estimates of the partitioned time stepping method for the evolutionary Stokes-Darcy flows

This paper analyzes some new error estimates for a backward Euler, partitioned time stepping algorithm, which was proposed in Mu and Zhu (2010) for the non-stationary Stokes-Darcy problem with Beavers-Joseph-Saffman interface condition. The well-known MINI elements and the linear Lagrangian elements are used in the fluid flow region and the porous media flow region, respectively. We prove that the error estimates for the fluid velocity and the piezometric head in L2 norm are optimal. Moreover, under a modest time step restriction Δt≤C, we prove that the error estimates for the fluid velocity and the piezometric head in H1 norm are Δt78+h and for the pressures in L2 norm are Δt34+h, respectively.