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Numerical Convergence of the MPFA O-Method for General Quadrilateral Grids in Two and Three Dimensions

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Compatible Spatial Discretizations

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 142))

Abstract

This paper presents the MPFA O-method for quadrilateral grids, and gives convergence rates for the potential and the normal velocities. The convergence rates are estimated from numerical experiments. If the potential is in H 1+α, α>0, the found L 2 convergence order on rough grids in physical space is min{2, 2α} for the potential and min{1, α} for the normal velocities. For smooth grids the convergence order for the normal velocities increases to min{2,α}. The O-method is exact for uniform flow on rough grids. This also holds in three dimensions, where the cells may have nonplanar surfaces.

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Author information

Authors and Affiliations

  1. Center for Integrated Petroleum Research, University of Bergen, NO-5020, Bergen, Norway

    Ivar Aavatsmark

Authors
  1. Ivar Aavatsmark
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  2. Geir Terje Eigestad
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  3. Runhild Aae Klausen
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Editor information

Editors and Affiliations

  1. Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN, 55455, USA

    Douglas N. Arnold

  2. Computational Mathematics and Algorithms Department, Sandia National Laboratories, Alburquerque, NM, 87185-1110, USA

    Pavel B. Bochev  & Richard B. Lehoucq  & 

  3. Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213-3890, USA

    Roy A. Nicolaides

  4. Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    Mikhail Shashkov

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© 2006 Springer Science+Business Media, LLC

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Aavatsmark, I., Eigestad, G.T., Klausen, R.A. (2006). Numerical Convergence of the MPFA O-Method for General Quadrilateral Grids in Two and Three Dimensions. In: Arnold, D.N., Bochev, P.B., Lehoucq, R.B., Nicolaides, R.A., Shashkov, M. (eds) Compatible Spatial Discretizations. The IMA Volumes in Mathematics and its Applications, vol 142. Springer, New York, NY. https://doi.org/10.1007/0-387-38034-5_1

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