In this paper, we develop the numerical theory of decoupled modified characteristic FEMs for the fully evolutionary Navier–Stokes–Darcy model with the Beavers–Joseph interface condition. Based on lagging interface coupling terms, the system is decoupled, which means that the Navier–Stokes equations and the Darcy equation are solved in each time step, respectively. In particular, the Navier–Stokes equations are solved by the modified characteristic FEMs, which overcome the computational inefficiency and analytical difficulties caused by the nonlinear term. Then we prove the optimal $L^2$-norm error convergence order of the solutions by mathematical induction, whose proof implies the uniform $L^{\infty }$-boundedness of the fully discrete velocity solution. Finally some numerical tests are presented to show high efficiency of this method.

在本文中，我们开发了具有Beavers-Joseph界面条件的完全演化Navier-Stokes-Darcy模型的解耦修饰特征有限元法的数值理论。基于滞后的界面耦合项，系统解耦，这意味着分别在每个时间步求解Navier–Stokes方程和Darcy方程。尤其是，Navier-Stokes方程是通过修改后的特征有限元法解决的，它克服了非线性项引起的计算效率低和分析困难。然后证明最优${\mathrm{大号}}^2$归纳的-范数误差收敛阶的数学归纳法，其证明意味着一致 ${\mathrm{大号}}^{\infty }$离散速度解的有界性 最后，通过一些数值试验证明了该方法的高效率。