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Numerical discretization of a Darcy–Forchheimer model

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Abstract

We solve a steady Darcy–Forchheimer flow in a bounded region by means of piecewise constant velocities and nonconforming piecewise \({\mathbb{P}_1}\) pressures. For the computation, we solve the nonlinearity by an alternating-directions algorithm and we decouple the computation of the velocity from that of the pressure by a gradient algorithm. We prove a priori error estimates of the scheme and convergence of the alternating-directions algorithm.

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Authors and Affiliations

  1. UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 75005, Paris, France

    V. Girault

  2. Institute for Computational Engineering and Sciences, Center for Subsurface Modelling, The University of Texas at Austin, Austin, TX, 78712-0027, USA

    M. F. Wheeler

Authors
  1. V. Girault
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  2. M. F. Wheeler
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Correspondence to V. Girault.

Additional information

The first author was supported by the J. Tinsley Oden Faculty Fellowship, ICES, The University of Texas at Austin.

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Girault, V., Wheeler, M.F. Numerical discretization of a Darcy–Forchheimer model. Numer. Math. 110, 161–198 (2008). https://doi.org/10.1007/s00211-008-0157-7

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  • DOI: https://doi.org/10.1007/s00211-008-0157-7

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