Decoupled scheme with different time step sizes for the evolutionary Stokes-Darcy model

In this report, a partitioned time stepping algorithm which allows different time steps in the fluid region and the porous region is analyzed for the fully evolutionary Stokes-Darcy problem. This method requires only one, uncoupled Stokes and Darcy sub-physics and sub-domain solve per time step. Under a modest time step restriction of the form 4t ≤ C where C = C(physical parameters) we prove zero-stability of the method. We also derive error estimates. Numerical tests given confirming the convergence theory and demonstrating the computational efficiency of the partitioned method.