LDG Method For Partial Differential Equations Based On Triangular Meshes

The discontinuous Galerkin method for various partial differential equations has been one of the highlights in the study of numerical methods, and has been applied to the fields of science and engineering widely in recent years. In this paper, LDG method is used to solve the two-dimensional elliptic equationUnder the uniform rectangular meshes, u is p＋2-order superconvergent at the right Radau points based on LDG method. On the other hand, under the uniform triangular meshes,(?) can achieve the p＋1-order superconvergence at the nodes compared with the p＋1/2-order convergence in L₂-norm, based on LDG method.Further LDG method under the uniform triangular meshes is implemented to solve the two-dimensional convection-diffusion equationThe existence and uniqueness of the LDG solutions are verified first, The following error estimates are observed numerically, i.e.