Analysis of A New Variable Time-stepping Time Filter Algorithm for The Unsteady Stokes/Darcy Model

In this report, we first present a first order ${\theta}$-scheme with the variable time steps which is one parameter family of Linear Multi-step methods for the unsteady Stokes/Darcy model. On the basis of this scheme, we use a time filter algorithm to increase the convergence order to the second order with almost no increasing the amount of computation, from which we get a new efficient algorithm. Then we analyze stabilities and the second-order accuracy of variable time-stepping algorithms of coupled and decoupled Linear Multi-step methods plus time filters, respectively. Finally, the theoretical results including effectiveness, convergence and efficiency are verified by several numerical experiments.