Optimal long time error estimates of a second-order decoupled finite element method for the Stokes–Darcy problem

Abstract

In this paper, we propose a second-order decoupled finite element method based on lagging a part of the interfacial coupling terms for the time dependent Stokes–Darcy problem, which only need to solve two sub-physical problems sequentially. Under a modest time step restriction Δt≤C(physical parameters), the optimal long time error estimates are obtained both in the L2 norm and in the H1 norm. Numerical results are provided to illustrate the convergence rate O(Δt2) of the temporal approximation.