caa a22 4500 463177770 CHVBK 20180406164830.0 cr unu---uuuuu 170326e20071201xx s 000 0 eng 10.1007/s10596-007-9056-8 doi (NATIONALLICENCE)springer-10.1007/s10596-007-9056-8 Convergence of a symmetric MPFA method on quadrilateral grids [Elektronische Daten] [I. Aavatsmark, G. Eigestad, R. Klausen, M. Wheeler, I. Yotov] This paper investigates different variants of the multipoint flux approximation (MPFA) O-method in 2D, which rely on a transformation to an orthogonal reference space. This approach yields a system of equations with a symmetric matrix of coefficients. Different methods appear, depending on where the transformed permeability is evaluated. Midpoint and corner-point evaluations are considered. Relations to mixed finite element (MFE) methods with different velocity finite element spaces are further discussed. Convergence of the MPFA methods is investigated numerically. For corner-point evaluation of the reference permeability, the same convergence behavior as the O-method in the physical space is achieved when the grids are refined uniformly or when grid perturbations of order h 2 are allowed. For h 2-perturbed grids, the convergence of the normal velocities is slower for the midpoint evaluation than for the corner-point evaluation. However, for rough grids, i.e., grids with perturbations of order h, contrary to the physical space method, convergence cannot be claimed for any of the investigated reference space methods. The relations to the MFE methods are used to explain the loss of convergence. Springer Science+Business Media B.V., 2007 Mixed finite element method nationallicence Multipoint flux approximation nationallicence Control-volume method nationallicence Aavatsmark I. Centre for Integrated Petroleum Research, University of Bergen, P.O. Box 7800, 5020, Bergen, Norway aut Eigestad G. Centre for Integrated Petroleum Research, University of Bergen, P.O. Box 7800, 5020, Bergen, Norway aut Klausen R. Centre for Integrated Petroleum Research, University of Bergen, P.O. Box 7800, 5020, Bergen, Norway aut Wheeler M. Institute for Computational Engineering and Sciences (ICES), Department of Aerospace Engineering & Engineering Mechanics, and Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, 78712, Austin, TX, USA aut Yotov I. Department of Mathematics, 301 Thackeray Hall, University of Pittsburgh, 15260, Pittsburgh, PA, USA aut Computational Geosciences Springer Netherlands 11/4(2007-12-01), 333-345 1420-0597 11:4<333 2007 11 10596 https://doi.org/10.1007/s10596-007-9056-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10596-007-9056-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Aavatsmark I. Centre for Integrated Petroleum Research, University of Bergen, P.O. Box 7800, 5020, Bergen, Norway aut NATIONALLICENCE 700 1- Eigestad G. Centre for Integrated Petroleum Research, University of Bergen, P.O. Box 7800, 5020, Bergen, Norway aut NATIONALLICENCE 700 1- Klausen R. Centre for Integrated Petroleum Research, University of Bergen, P.O. Box 7800, 5020, Bergen, Norway aut NATIONALLICENCE 700 1- Wheeler M. Institute for Computational Engineering and Sciences (ICES), Department of Aerospace Engineering & Engineering Mechanics, and Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, 78712, Austin, TX, USA aut NATIONALLICENCE 700 1- Yotov I. Department of Mathematics, 301 Thackeray Hall, University of Pittsburgh, 15260, Pittsburgh, PA, USA aut NATIONALLICENCE 773 0- Computational Geosciences Springer Netherlands 11/4(2007-12-01), 333-345 1420-0597 11:4<333 2007 11 10596 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer