A Modified Weak Galerkin Finite Element Method For The Primal Second-order Elliptic Equations

In this paper,we use a modified weak Galerkin finite element method to solve the second order elliptic equations.The main idea of this method is using the average of the internal functions to replace the boundary functions.So this method has many advan-tages.Firstly,weak function space is approximated by piecewise discontinuous polynomial and the finite element partition can be polytopal or polygon partition,these make the modified weak Galerkin finite element method more flexible and wide in the application.Secondly,the boundary functions are represented by the average of the interior functions on each element,so the degrees of freedom can be reduced in the whole discrete system.Finally,we can obtain the optimal order of the convergence of estimate.In the paper,the basic principle and theoretical analysis of the modified weak Galerkin finite element method are introduced.At the same time,we achieve the algorithms,stability and error estimate of the three kinds of boundary value conditions,respectively.In the end,the convergence of the numerical solution uh in the norm of L2 and H1 is o(H^k+1)and o?H^k?.