A Domain Decomposition Method With Weak Galerkin For A Coupled Dual-Porosity-Stokes Problem

In this paper,the weak Galerkin method combined with the iterative domain decomposition algorithm is used to solve the problem of the Dual-Porosity-Stokes coupled model with Beavers-Joseph-Saffman interface condition.Firstly,we give the model and the variational form of the original problem,then the corresponding Robin boundary conditions on the interface for the Dual-Porosity region and Stokes region respectively.Furthermore,a complete Robin-Robin domain decomposition method is given for the model.The weak Galerkin element numerical scheme of the original problem is obtained by the definitions of the weak function space and the relevant operators.After defining the norm in the weak finite element space,inf-sup condition along with the existence and uniqueness of WG numerical solution are proved.Finally,the effectiveness of the iterative domain decomposition method based on WG for solving the Dual-Porosity-Stokes coupled problem is verified by severial different numerical examples.