A Hybridized Weak Galerkin Mixed Finite Element Method For Second-order Elliptic Equations

In this paper,we present a hybridized weak Galerkin(HWG)mixed finite element method for solving the second-order elliptic equations with Neumann and Robin bound-ary conditions.Inherit the WG’ s ideas,weak functions are used and the differential operators are approximated by their weak forms as distributions,and a stabilizer is intro-duced to maintain the weak continuity of the numerical solution.It makes the method flexible and efficient.On this basis,the Lagrange multiplier is introduced,and the unit internal function is represented by the unit boundary function to reduce the dimension of the discrete system.Finally,optimal order error estimates could be established for the corresponding HWG finite element approximations for both primal variables and the Lagrange multipliers.