Analysis of a new adaptive time filter algorithm for the unsteady Stokes/Darcy model

In this article, we propose a new adaptive time filter algorithm for the unsteady Stokes/Darcy model. Firstly, we present a first order 0-scheme with variable time step which is one parameter family of Linear Multi-step method. Furthermore, using time filter scheme, the convergence order is increased to the second order without almost increasing the extra computation. Moreover, we construct decoupled and coupled adaptive algorithms to improve the computational efficiency. Theoretically, we analyze stability and the second-order accuracy of Linear Multi-step method plus time filter with non-increasing variable time step, respectively. Finally, numerical experiments are given to verify theoretical results, including effectiveness, convergence and efficiency.