A Conforming Discontinuous Galerkin Finite Element Method For Second Order Parabolic Equations

In this paper,we research the Conforming Discontinuous Galerkin finite element method(CDG method).This method is based on the traditional weak Galerkin finite element method,and removes the stabilizer in the numerical scheme.In order to ensure the weak continuity of the numerical solution,the order of weak differential operators is increased.At the same time,the boundary functions are replaced by the average of the internal functions,thereby the boundary degree of freedom is reduced.This strategy not only makes the scheme simpler,but also lowers the calculated complexity.By taking the parabolic equation as an example,we introduce the mathematical theory of the CDG method in detail.Firstly,the semi-discrete and fully discrete numerical schemes of the equation and the well-poseness of the numerical schemes are presented.Then,the corresponding error equations for the both numerical schemes are established,and the opti-mal order error estimates of L~2 and H~1 are provided respectively.Finally,through numerical experiments with triangle partition and polygon partiton,the theoretical results of the CDG method are verified.