A covolume method is proposed for the mixed formulation of second-order elliptic problems. The solution domain is divided by a quadrilateral grid, corresponding to which a nonoverlapping dual grid is constructed. The velocity and pressure are approximated by the lowest-order Raviart–Thomas space on quadrilaterals. We prove its first order optimal rate of convergence for the approximate velocities in the -norm as well as for the approximate pressures in the -norm. A second order error estimate between a suitable projection of the exact velocity (or pressure) and the approximate velocity (or approximate pressure) is also presented. Numerical experiments are provided to illustrate the error behavior of the scheme.
This work of the last author was partially supported by the National Natural Science Foundation of China (Grant No. 11126040), and the National Natural Science Foundation of China (Grant No. 11301214).