Superconvergence of mixed covolume method on quadrilateral grids for elliptic problems

This paper considers the mixed covolume method for the second-order elliptic equations over quadrilaterals. Superconvergence results are established in this paper on quadrilateral grids satisfying the h ²-parallelogram condition when the lowest-order Raviart-Thomas space is employed in the mixed covolume method. The authors prove O(h ²) accuracy between the approximate velocity or pressure and a suitable projection of the real velocity or pressure in the L ² norm. Numerical experiments illustrating the theoretical results are provided.