Primal vs dual variable approach for mixed-hybrid finite element approximation of the potential fluid flow problem in porous media

Abstract

Mixed-hybrid finite element discretization of the Darcy’s law and the continuity equation that describe the potential fluid flow problem in porous media leads to symmetric but indefinite linear systems for the velocity and pressure vector components. In this contribution we compare the computational efficiency of two main techniques for the solution of such systems based on a cheap elimination of a portion of variables and on subsequent iterative solution of a transformed system. We consider Schur complement reduction and null-space based projection. Since for both approaches the asymptotic convergence factor in the iterative part depends linearly on the mesh size parameter, we perform computational experiments on several real-world problems and report a comparison of numerical results which includes not only the cost of iterative part but also the overhead of initial transformation and back substitution process.