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Discontinuous Galerkin and mimetic finite difference methods for coupled Stokes–Darcy flows on polygonal and polyhedral grids

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Abstract

We study locally mass conservative approximations of coupled Darcy and Stokes flows on polygonal and polyhedral meshes. The discontinuous Galerkin (DG) finite element method is used in the Stokes region and the mimetic finite difference method is used in the Darcy region. DG finite element spaces are defined on polygonal and polyhedral grids by introducing lifting operators mapping mimetic degrees of freedom to functional spaces. Optimal convergence estimates for the numerical scheme are derived. Results from computational experiments supporting the theory are presented.

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Authors and Affiliations

  1. Applied Mathematics and Plasma Physics Group, Theoretical Division, Los Alamos National Laboratory, Mail Stop B284, Los Alamos, NM, 87545, USA

    Konstantin Lipnikov

  2. Mathematics Research Institute, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, EX4 4QF, UK

    Danail Vassilev

  3. Department of Mathematics, 301 Thackeray Hall, University of Pittsburgh, Pittsburgh, PA, 15260, USA

    Ivan Yotov

Authors
  1. Konstantin Lipnikov
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  2. Danail Vassilev
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  3. Ivan Yotov
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Correspondence to Danail Vassilev.

Additional information

K. Lipnikov was partially supported by the DOE Office of Science Advanced Scientific Computing Research (ASCR) Program in Applied Mathematics.

I. Yotov was partially supported by the DOE Grant DE-FG02-04ER25618 and the NSF Grant DMS 1115856.

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Lipnikov, K., Vassilev, D. & Yotov, I. Discontinuous Galerkin and mimetic finite difference methods for coupled Stokes–Darcy flows on polygonal and polyhedral grids. Numer. Math. 126, 321–360 (2014). https://doi.org/10.1007/s00211-013-0563-3

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  • DOI: https://doi.org/10.1007/s00211-013-0563-3

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