Error Estimation And Projection Technique In Discontinuous Galerkin Method

This paper collects and collates the commonly used projection techniques for error analysis of discontinuous galerkin methods.Includes local L2 projection,Gauss-Radau projection,and generalized Gauss-Radau projection.This paper gives the correspond-ing existence,uniqueness and approximation properties of these projections.And ap-propriate promotion.For example,the Gauss-Radau projection and the generalized Gauss-Radau projection in the three-dimensional case.This paper proves that in the high-dimensional case,the numerical solution of the hyperbolic equation in the DG format and the numerical solution of the convection-diffusion equation in the LDG format can reach the optimal order.