A Weak Galerkin Mixed Finite Element Methods For The Convection-diffusion Equations

In this paper,we consider the weak Galerkin(WG)mixed finite element method(MFEM)for solving the second-order elliptic problems with the first-order term under several boundary conditions.The main idea of this method is to introduce the interme-diate variable to achieve the purpose of reducing the order of the equation.The weak finite element method is a new method to replace the differential operator in the original variational problem by the new weak differential operator.At the same time;polynomial polyhedron space and arbitrary polygon for different partial differential equations can be introduced into different.combinations to form different weak finite element,methods,and the introduction of stabilizer to ensure the weak continuity of the numerical solution.The mixed form of the finite element methods can reduce the order of partial differential equations,thus reducing the smoothness of finite element,space requirements,and get the solution of the discrete function and derivative function at the same time in the process of solving.On the basis of the existing WGFEM method,we introduce the first order term and the constant term and discuss the mixed form of WG under the three boundary conditions of Dirichlet,Neumann,and Robin.Then the theoretical foundation of weak finite element method in mixed form is further improved.