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Nitsche's type stabilization for the fully mixed Navier-Stokes/Darcy problem
Jiaping Yu,Yuhong Zhang
Keywords:Navier-Stokes/Darcy problem, Mixed finite elements, Nitsche's method, Beavers-Joseph-Saffman
      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 stabilization parameter $\delta$ for the optimal error estimates, while the numerical tests support the stability and efficiency of this stabilized mixed method.