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Journal of Scientific Computing

, Volume 77, Issue 3, pp 1605–1620 | Cite as

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

  • Guosheng Fu
  • Christoph Lehrenfeld
Article

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.

Keywords

HDG Stokes–Darcy Divergence-conforming Beavers–Joseph–Saffman 

Mathematics Subject Classification

65N30 65N12 76S05 76D07 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA
  2. 2.Institut für Numerische und Angewandte MathematikGöttingenGermany

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