A Discontinuous Galerkin Method For Solving Unsteady Convection Diffusion Equation

The Discontinuous Galerkin method(DG) for various problems has been one of the highlights in the study of numerical methods, due to the stability of the method.Actually, It has been applied to the filed of science and engineering in recent years.The Discontinuous Galerkin Method for solving steady convection diffusion equation has been widlly studied[10-20]. In this paper, we mainly discuss a Discontinuous Galerkin Method for solving unsteady convection diffusion equation, and the existence and uniquencess of the DG solution, we choose some special numerical traces as those in papers[11-12], using the numerical traces, we prove the existence and uniquencess of the DG solution. At the chapter four, we give the numerical result of the method, and the result has high accuracy. So, the method is effective for solving unsteady convection diffusion equation.