Error estimates of a second-order decoupled scheme for the evolutionary Stokes-Darcy system

摘要

This paper presents the new error estimates for a second-order backward-differentiation scheme (BDF2) given in [3] for the evolutionary Stokes-Darcy system. We prove the unconditional optimal error estimates and the uniform in time error estimates with the modest time step (Δt ≤ C) for the fluid velocity and the hydraulic head in L~2 norm. Besides, we also prove the error estimates for the fluid velocity and the hydraulic head in H~1 norm are Δt~(15/8) +h and the pressures in L~2 norms are Δt~(7/4) +h. Numerical tests are provided to illustrate the accuracy and validity of the decoupled scheme.