A characteristics-mixed covolume method for a convection-dominated transport problem

In this paper, we propose a characteristics-mixed covolume method for approximating the solution to a convection dominated transport problem. The method is a combination of characteristic approximation to handle the convection term in time and mixed covolume method spatial approximation to deal with the diffusion term. The velocity and press are approximated by the lowest order Raviart–Thomas mixed finite element space on rectangles. The projection of a mixed covolume element is introduced. We prove its first order optimal rate of convergence for the approximate velocities in the L2L2 norm as well as for the approximate pressures in the L2L2 norm.