Discontinuous Galerkin Method of the First Order Parabolic Differential Equation

This paper is concerned with the mathematical study of the discontinuous Galerkin (DG) finite element method for the parabolic differential equation. The DG method is a vital numerical method with much mass compensation and more flexible meshing than other methods. In this study, we give a general introduction and discuss about the discontinuous Galerkin Method of first order parabolic problem. The parabolic problem satisfies the condition of the existence and uniqueness of DG solution. The error analysis of this problem is also established. The main goal of this study is to theoretically explore the convergence of the solution of the above methods and show the validity of the results.