Hierarchical basis in $H^{div}$ space for a mixed finite element formulation of the Darcy problem

A mixed variational formulation based on a discontinuous Galerkin method for solving the Darcy problem with a tensor permeability coefficient is considered. Two special hierarchical basis systems in $H^{div}$ space for velocity and in $H^1$ space for pressure are constructed. The influence of these basis on the properties of the matrix of the discrete analogue is investigated.