Abstract
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 L2-norm error convergence order of the solutions by mathematical induction, whose proof implies the uniform L∞-boundedness of the fully discrete velocity solution. Finally some numerical tests are presented to show high efficiency of this method.
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