Discontinuous Galerkin Method of the Second Order Parabolic Differential Equation

This paper is concerned with the mathematical study of the discontinuous Galerkin finite element method for the parabolic differential equation. Finite element methods have been recognized as valuable in the numerical approximation of solutions to self-adjoint or nearly self-adjoint parabolic partial differential equation problems. The discontinuous Galerkin method is a vital numerical method with much mass compensation and more flexible meshing than other methods. These methods belong to a class of numerical methods for solving partial differential equations. They are based on weak formulations and with finite dimensional piecewise polynomial solution space and test function space. This study is focused on the discontinuous Galerkin method of the second 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 explore the convergence of the solution of the DG method and show the validity of the results.