Weak Galerkin Finite Element Method For The Coupled Darcy-Stokes Flow

A weak Galerkin finite element method for the coupled Darcy-Stokes flow system is proposed.Based on a well-defined discrete norm ‖·‖Vh and some suitable parame-ters,the existence and uniqueness of the weak Galerkin formulation are proven.For the errors eu=Qhu-uh={Q0u-u0,Qbu-ub},ep=QhP-Ph,The convergence esti-mates is obtained:‖eu‖Vh+‖ep‖(?)hβ+hγS+1+hγD+1,where the parameters β,γS,γD are some parameters related to the definitions of discrete spaces.The theoretical error estimate is confirmed by one numerical experiment.