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Discontinuous Finite Element Methods for Coupled Surface–Subsurface Flow and Transport Problems

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Book cover Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 157))

Abstract

A numerical method is proposed to solve the coupled flow and transport problems in adjacent surface and subsurface regions. The flow problem is characterized by the Navier–Stokes (or Stokes) equations coupled by Darcy equations. In the subsurface, the diffusion coefficient of the transport equation depends on the velocity field in a nonlinear manner. The interior penalty discontinuous Galerkin method is used for the spatial discretization, and the backward Euler technique for the time integration. Convergence of the scheme is theoretically derived. Numerical examples show the robustness of the method for heterogeneous and fractured porous media.

AMS(MOS) subject classifications. 65M60, 76S05, 76D05

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Acknowledgements

The author acknowledges the support of National Science Foundation through the grant DMS 0810422.

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Authors and Affiliations

  1. Department of Computational and Applied Mathematics, Rice University, 6100 Main St MS-134, Houston, TX, 77005, USA

    Beatrice Riviere

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  1. Beatrice Riviere
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Correspondence to Beatrice Riviere .

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Editors and Affiliations

  1. Department of Mathematics, The University of Tennessee, Knoxville, Tennessee, USA

    Xiaobing Feng

  2. Department of Mathematics, The University of Tennessee, Knoxville, Tennessee, USA

    Ohannes Karakashian

  3. Department of Mathematics, The University of Tennessee, Knoxville, Tennessee, USA

    Yulong Xing

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Riviere, B. (2014). Discontinuous Finite Element Methods for Coupled Surface–Subsurface Flow and Transport Problems. In: Feng, X., Karakashian, O., Xing, Y. (eds) Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations. The IMA Volumes in Mathematics and its Applications, vol 157. Springer, Cham. https://doi.org/10.1007/978-3-319-01818-8_11

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