Error Analysis of the Second Order Time Dependent Parabolic Equation by Using Discontinuous Galerkin Method

Abstract

The paper is offered a mathematical study to establish the error estimate of the numerical solution by applying discontinuous Galerkin (DG) finite element method of the second order time dependent parabolic equation. The DG method is an exciting numerical method with much mass compensation and more flexible meshing than other numerical methods. This study is stated a general introduction and discuss about the discontinuous Galerkin Method for the time dependent parabolic scheme. The method is well suited for large scale time-dependent computations in which high accuracy is required. The discontinuous Galerkin (DG) method has been extensively studied and applied to a wide range of parabolic problems. The main objective of this study is to theoretically explore the convergence of the solution as well as to adjust the error estimate of the methods and display the validity of the results. Two numerical experiments are shown that validate the efficiency of the method.

Journal of Engineering Science 15(2), 2024, 113-120