Weak Galerkin Method For The Dual-Porosity-Stokes Model

This paper introduces a weak Galerkin(WG)finite element method for the DualPorosity-Stokes model.The Dual-Porosity model involves two kinds of pressures,namely the matrix pressure and the microfracture pressure,and they describe the flow in porous media.The Dual-Porosity-Stokes model couples the Dual-Porosity equations with the Stokes equations through four physically effective interface conditions.By solving this model with WG method,we first introduce the Dual-Porosity-Stokes model,and several weak Galerkin finite element spaces.Then the definitions of the discrete weak gradient operator and the discrete weak divergence operator are provided.We subsequently propose the weak Galerkin finite element numerical scheme for the model,and prove the inf-sup condition,the existence and uniqueness of the WG numerical solutions.Furthermore,the error equation and the corresponding optimal order error estimate are presented.Ultimately,by completing several numerical experiments,the effectiveness of the weak Galerkin method to solve the Dual-Porosity-Stokes model is verified.