Convergence of an upwind control-volume mixed finite element method for convection-diffusion problems (Q2471835)

The author considers an upwind control volume mixed finite element method for convection-diffusion problem on rectangular grids. Based on the lowest order Raviart-Thomas mixed finite element space as the trial functional space and associate control-volumes, or covolumes, with the vector variable as well as the scalar variable, he gives a first order convergence for both the vector variable as well as the scalar variable in discrete L2-norms. The results in this paper improve that of \textit{S.-H. Chou} et al. [SIAM J. Sci. Comput. 21, No. 1, 145--165 (1999; Zbl 0947.65120)].