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A Strongly Conservative Hybrid DG/Mixed FEM for the Coupling of Stokes and Darcy Flow

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Abstract

We consider the coupling of free and porous media flow governed by Stokes and Darcy equations with the Beavers–Joseph–Saffman interface condition. This model is discretized using a divergence-conforming finite element for the velocities in the whole domain. Hybrid discontinuous Galerkin techniques and mixed methods are used in the Stokes and Darcy subdomains, respectively. The discretization achieves mass conservation in the sense of \(H(\mathrm {div},\Omega )\), and we obtain optimal velocity convergence. Numerical results are presented to validate the theoretical findings.

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Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, 182 George St, Providence, RI, 02912, USA

    Guosheng Fu

  2. Institut für Numerische und Angewandte Mathematik, Lotzestr. 16-18, 37083, Göttingen, Germany

    Christoph Lehrenfeld

Authors
  1. Guosheng Fu
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  2. Christoph Lehrenfeld
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Correspondence to Guosheng Fu.

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Dedicated to the 60th birthday of Professor Bernardo Cockburn.

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Fu, G., Lehrenfeld, C. A Strongly Conservative Hybrid DG/Mixed FEM for the Coupling of Stokes and Darcy Flow. J Sci Comput 77, 1605–1620 (2018). https://doi.org/10.1007/s10915-018-0691-0

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  • DOI: https://doi.org/10.1007/s10915-018-0691-0

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