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Adaptive Discontinuous Galerkin Methods for Flow in Porous Media

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Numerical Mathematics and Advanced Applications ENUMATH 2017 (ENUMATH 2017)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 126))

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Abstract

We present an adaptive Discontinuous Galerkin discretization for the solution of porous media flow problems. The considered flows are immiscible and incompressible. The fully adaptive approach implemented allows for refinement and coarsening in both the element size, the polynomial degree and the time step size.

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Acknowledgements

Birane Kane would like to thank the German Research Foundation (DFG) for financial support of the project within the Cluster of Excellence in Simulation Technology (EXC 310/1) at the University of Stuttgart. Robert Klöfkorn acknowledges the Research Council of Norway and the industry partners; ConocoPhillips Skandinavia AS, Aker BP ASA, Eni Norge AS, Maersk Oil Norway AS, DONG Energy A/S, Denmark, Statoil Petroleum AS, ENGIE E&P NORGE AS, Lundin Norway AS, Halliburton AS, Schlumberger Norge AS, Wintershall Norge AS, DEA Norge AS of The National IOR Centre of Norway for support. The authors would like to thank the reviewers for helpful comments to improve this work.

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Authors and Affiliations

  1. Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Stuttgart, Germany

    Birane Kane

  2. International Research Institute of Stavanger, Stavanger, Norway

    Robert Klöfkorn

  3. Mathematics Institute, University of Warwick, Coventry, UK

    Andreas Dedner

Authors
  1. Birane Kane
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  2. Robert Klöfkorn
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  3. Andreas Dedner
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Corresponding author

Correspondence to Birane Kane .

Editor information

Editors and Affiliations

  1. University of Bergen, Bergen, Norway

    Florin Adrian Radu

  2. University of Bergen, Bergen, Norway

    Kundan Kumar

  3. University of Bergen, Bergen, Norway

    Inga Berre

  4. University of Bergen, Bergen, Norway

    Jan Martin Nordbotten

  5. Hasselt University, Diepenbeek, Belgium

    Iuliu Sorin Pop

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Kane, B., Klöfkorn, R., Dedner, A. (2019). Adaptive Discontinuous Galerkin Methods for Flow in Porous Media. In: Radu, F., Kumar, K., Berre, I., Nordbotten, J., Pop, I. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2017. ENUMATH 2017. Lecture Notes in Computational Science and Engineering, vol 126. Springer, Cham. https://doi.org/10.1007/978-3-319-96415-7_32

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