Mixed stabilized finite element method for the stationary Stokes-dual-permeability fluid flow model

This article proposes a stabilized mixed finite element method to investigate the stationary Stokes-dual-permeability fluid flow model which couples the free flow region modeled by the Stokes equations and dual-porous medium modeled by the dual-permeability equations. The robust mixed finite element method developed here does not require any Lagrange multiplier but a mesh dependent stabilization term with a relaxation parameter is introduced essentially to ensure the numerical stability of the algorithm. The well-posedness and the optimal error estimate of the finite element scheme are derived. Furthermore, an iterative scheme is developed based on the traditional coupled algorithm. We prove that the iterative scheme converges to the coupled scheme, and the rate of convergence is estimated. The feature of the model is illustrated by considering five numerical examples which reveal the applicability of the fluid flow model as well as the accuracy of the numerical method.