Abstract
In this paper, we present and analyze a fully mixed finite element scheme for the Navier-Stokes/Darcy problem based on the Nitsche's type interface stabilizations, in the fluid region coupled with the porous media domain. The reasonable parameter $ \delta>0 $, which is independent of mesh size $ h $, will guarantee the stability and optimal convergence of our stabilized scheme. Moreover, we explicitly derive the dependence and requirement of the stabilization parameter $ \delta $ for the optimal error estimates, while the numerical tests support the stability and efficiency of this stabilized mixed method.
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