A New Kind Of Discontinuous Galerkin Finite Element Method In The Application Of Reaction Diffusion Equations

In this paper, a new stabilized discontinuous Galerkin method within a new functionspace setting is introduced, which involves an extra stabilization term on the normalfuxes across the element interfaces. It is diferent from the general DG methods. Theformulation satisfes a local conservation property and we prove well posedness of the newformulation by Inf-Sup condition. A priori error estimates and a posteriori error estimatesare derived. At last, a2D experiment is given to prove the rationality of the method.