Characteristic Discontinuous Finite El-ement Methods For Convection Diffu-sion Problems

In this article, we mainly consider the numerical simulation of convection dominated diffusion equation. The equation is Widely used in many aspects of our daily life, especially in the groundwater literature. Standard finite element and finite difference methods usually exhibit some combination of nonphysical oscillation and excessive numerical dispersion. Many numerical methods have been developed to overcome these difficulties. In this paper we utilize the characteristics method and combine it with interior penalty discontinuous Galerkin method to solve the convection diffusion problems. The characteristic discontinuous finite element method proposes the conceptual and computational merits of both characteristics method and interior penalty discontinuous Galerkin method, and it can deal with strong convection domi-nated problems effectively. We present a first order and a new second order accuracy in time increment full discrete character IPDG formation for convection diffusion problems. Optimal error estimates are proved in the paper. Finally, numerical results are presented for the first order accuracy method, which verify the error estimates and show the efficiency of the provided method.