Decoupled time filtered method for the time dependent Stokes–Biot problem

In this paper, we propose a novel decoupled time filtered finite element method for the coupled Stokes–Biot problem. The key innovation of our method is the combination of a decoupling strategy with a time filtered technique that can enhance computational efficiency while maintaining numerical accuracy. Specifically, applying the time filter to the backward Euler scheme elevates its temporal accuracy to second order. At each time step, we first solve the Stokes problem, then use the computed Stokes velocity to solve the Biot problem. We rigorously analyze the proposed scheme to establish its stability and derive error estimates. Furthermore, some numerical tests are presented to validate the theoretical findings and demonstrate the efficiency, accuracy, and robustness of our method.