Error Ertimates Of Discontinuous Galerkin Method For Nonlinear Convection-diffusion Equations

As a numerical method for solving partial differential equations,discontinuous Galerkin method has the advantages of high accuracy and high resolution,and has been widely used in many fields.In this work,the DG method is used to solve a class of nonlinear convection-diffusion equations.The stability and convergence order of the method are verified by numerical experiments.The main contents of this work are given in the third and fourth chapters.In the third,fourth chapters,the spatial semi-discrete numerical schemes for solving nonlinear convection diffusion equations by DG method are given from the theoretical point of view,and the detailed stability analysis and error estimation are carried out in the form of the scheme.In the process of error analysis,the convergence order of the numerical scheme is proved by introducing the projection in the error analysis.In the fifth chapter,from the perspective of the numerical experiment,the explicit third order TVD Runge-Kutta method is used for the numerical scheme in the second,third-chapter and the fully discrete numerical scheme is obtained which verifies the theoretical results.