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Solution of Augmented Systems from a Mixed-hybrid Finite Element Discretization of the Potential Fluid Flow Problem: Asymptotic Rates of Convergence

In the paper we consider several approaches for solving linear systems from a mixed-hybrid nite element discretization of the Darcy's law and the continuity equation describing the potential uid ow in porous media. Spectral properties of resulting symmetric but indeenite systems in terms of a mesh size parameter are discussed and the asymptotic rate of convergence of iterative solvers applied either to whole indeenite system, to successive Schur complement systems or to systems projected onto certain null-spaces is estimated.