Application of the satisfying Babuska-Brezzi method to a two dimensional diffusion problem

The satisfying Babuska—Brezzi(SBB) method is applied to a two-dimensional diffusion problem. Several interpolation schemes, both continuous and discontinuous, are investigated numerically. The superconvergence phenomenon observed in the one-dimensional case is not recovered in two dimensions. However, SBB does stabilize the numerical solution substantially, particularly for low-order interpolations