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

  • Beatrice RiviereEmail author
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 157)


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.


Navier–Stokes Darcy Transport Discontinuous Galerkin Heterogeneous media Convergence Multinumerics 



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


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Computational and Applied MathematicsRice UniversityHoustonUSA

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