Numerische Mathematik

, Volume 141, Issue 2, pp 353–397 | Cite as

Convergence analysis of a family of ELLAM schemes for a fully coupled model of miscible displacement in porous media

  • Hanz Martin ChengEmail author
  • Jérôme Droniou
  • Kim-Ngan Le


We analyse the convergence of numerical schemes in the GDM–ELLAM (Gradient Discretisation Method–Eulerian Lagrangian Localised Adjoint Method) framework for a strongly coupled elliptic-parabolic PDE which models miscible displacement in porous media. These schemes include, but are not limited to, Mixed Finite Element–ELLAM and Hybrid Mimetic Mixed–ELLAM schemes. A complete convergence analysis is presented on the coupled model, using only weak regularity assumptions on the solution (which are satisfied in practical applications), and not relying on \(L^\infty \) bounds (which are impossible to ensure at the discrete level given the anisotropic diffusion tensors and the general grids used in applications).

Mathematics Subject Classification

65M08 65M12 65M25 65M60 76S05 



this research was supported by the Australian Government through the Australian Research Council’s Discovery Projects funding scheme (Project Number DP170100605).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Hanz Martin Cheng
    • 1
    Email author
  • Jérôme Droniou
    • 1
  • Kim-Ngan Le
    • 2
  1. 1.School of Mathematical SciencesMonash UniversityClaytonAustralia
  2. 2.School of Mathematics and StatisticsThe University of New South WalesSydneyAustralia

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