Two low order characteristic finite element methods for a convection-dominated transport problem

Two low order rectangular finite elements for the convection diffusion problem with a modified characteristic finite element scheme are studied in this paper. The O.h2/ order error estimates in L2-norm with respect to the space are obtained for one element with regular meshes and the other under anisotropic meshes. In the process, we use some distinct properties of the interpolation operator, the integral identity technique and the mean value technique, instead of the traditional elliptic projection which is an indispensable tool in the convergence analysis of the previous literature. Finally, some numerical results are provided to verify our theoretical analysis.