A class of improved characteristic finite element method for convection-diffusion equation

摘要

Characteristics finite element methods have been proved available for numerical approximation of convection-diffusion equations. All of the existed schemes of characteristic finite element or finite difference methods are limited to have only one order accuracy in time increment. In this paper, we introduce a new variational formulation after some important modification for convection and diffusion terms. Then we proposed a class of characteristic finite element scheme from the variation formulation. We also prove that the proposed scheme has second order accuracy in time increment and the optimal errr estimates in both of H~1 and L~2 norms.