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Modeling fractures as interfaces with nonmatching grids

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Abstract

We consider a model for fluid flow in a porous medium with a fracture. In this model, the fracture is treated as an interface between subdomains, on which specific equations have to be solved. In this article, we analyze the discrete problem, assuming that the fracture mesh and the subdomain meshes are completely independent, but that the geometry of the fracture is respected. We show that despite this nonconformity, first-order convergence is preserved with the lowest-order Raviart–Thomas(-Nedelec) mixed finite elements. Numerical simulations confirm this result.

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Authors and Affiliations

  1. ENIT-LAMSIN, BP 37, 1002, Tunis-le Belvédère, Tunisia

    Najla Frih & Ali Saâda

  2. LMAC, UTC, Royallieu, BP 20 529, 60 205, Compiegne CEDEX, France

    Vincent Martin

  3. INRIA-Paris Rocquencourt, BP 105, 78153, Le Chesnay CEDEX, France

    Jean Elizabeth Roberts

Authors
  1. Najla Frih
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  2. Vincent Martin
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  3. Jean Elizabeth Roberts
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  4. Ali Saâda
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Correspondence to Jean Elizabeth Roberts.

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Frih, N., Martin, V., Roberts, J.E. et al. Modeling fractures as interfaces with nonmatching grids. Comput Geosci 16, 1043–1060 (2012). https://doi.org/10.1007/s10596-012-9302-6

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  • DOI: https://doi.org/10.1007/s10596-012-9302-6

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