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Analysis of an interior penalty discontinuous Galerkin scheme for two phase flow in porous media with dynamic capillary effects

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Abstract

We present an interior penalty discontinuous Galerkin scheme for a two-phase porous media flow model that incorporates dynamic effects in the capillary pressure. The approximation of the mass-conservation laws is performed in their original formulation, without introducing a global pressure. We prove the existence of a solution to the emerging fully discrete systems and the convergence of the scheme. Error-estimates are obtained for sufficiently smooth data.

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Acknowledgments

Stefan Karpinski wants to thank Prof. B.I. Wohlmuth for the introduction to this interesting topic and the guidance through his first years in academia. He would also like to express his gratitude to his employers, Dr. Roman Rojko and Dr. Stefan Zaprianov from ESPRiT Engineering GmbH for their mentorship and support. Special thanks also to Prof. F.A. Radu (Bergen) for the fruitful and productive discussions during his visit to the University of Bergen. This stay was supported by the International Research Training Group NUPUS, funded by the German Research Foundation DFG (GRK 1398), the Netherlands Organization for Scientific Research NWO (DN 81-754) and by the Research Council of Norway (215627). Iuliu Sorin Pop acknowledges the support from the Akademia grant of Statoil and from the Shell-NWO/FOM CSER programme (project 14CSER016).

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Authors and Affiliations

  1. ESPRiT Engineering GmbH, Munich, Germany

    Stefan Karpinski

  2. Faculty of Sciences, Hasselt University, Hasselt, Belgium

    Iuliu Sorin Pop

  3. Department of Mathematics, University of Bergen, Bergen, Norway

    Stefan Karpinski & Iuliu Sorin Pop

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  1. Stefan Karpinski
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Correspondence to Stefan Karpinski.

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Karpinski, S., Pop, I.S. Analysis of an interior penalty discontinuous Galerkin scheme for two phase flow in porous media with dynamic capillary effects. Numer. Math. 136, 249–286 (2017). https://doi.org/10.1007/s00211-016-0839-5

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