Partitioned time stepping method for time-fractional Stokes-Darcy model with the Beavers-Joseph-Saffman interface conditions

Abstract

This paper proposes a numerical method for solving the time-fractional Stokes-Darcy problem using a partitioned time stepping algorithm with the Beavers-Joseph-Saffman condition. The stability of the method is established under a moderate time step restriction, $\tau \le C$ where C represents physical parameters, by utilizing a discrete fractional Gronwall type inequality. Additionally, error estimates are derived to provide insight into the accuracy of the proposed method. Numerical experiments that support the theoretical results are presented.