Direct Discontinuous Galerkin Method For Elliptic Equation On Triangular Mesh

As one of the three basic partical differential equation,elliptic equation has many applications in engineering,such as normal heat conduction,the electric field and mag-netic field,etc.Because the boundary value problem of elliptic equation can be solved only in some special cases,it is important to find fast and efficient numerical methods.Discontinuous Galerkin finite element method(DG)is a kind of finite element method with piecewise polynomial basis function,is widely used in areas such as fluid mechanics because of the flexibility to handle complex geometric area and large defor-mation problems.Many new types of DG on the basis of DG method were put forward by development constantly.In the paper,DG method based on high precision numerical method and its basic properties were reviewed.DDG method directly on the approxima-tion of derivative value can reduce the amount of calculation and get better convergence.The high priecision numerical method is a kind of popular method for elliptic partial dif-ferential equations.The construction of DDG method was introduced in this paper,and gives the detail under the triangular mesh,elliptic partial differential equation of con-crete implementation,discusses the format parameter selection influence on numerical results,through the numerical experiment is consistent with the expected results.