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A non-symmetric coupling of the finite volume method and the boundary element method

Numerische Mathematik volume 135, pages 895–922 (2017)Cite this article

Abstract

As model problem we consider the prototype for flow and transport of a concentration in porous media in an interior domain and couple it with a diffusion process in the corresponding unbounded exterior domain. To solve the problem we develop a new non-symmetric coupling between the vertex-centered finite volume and boundary element method. This discretization provides naturally conservation of local fluxes and with an upwind option also stability in the convection dominated case. We aim to provide a first rigorous analysis of the system for different model parameters; stability, convergence, and a priori estimates. This includes the use of an implicit stabilization, known from the finite element and boundary element method coupling. Some numerical experiments conclude the work and confirm the theoretical results.

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Acknowledgments

F.-J. Sayas was partially supported by NSF Grant DMS 1216356.

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Authors and Affiliations

  1. Department of Mathematics, TU Darmstadt, Dolivostraße15, 64293, Darmstadt, Germany

    Christoph Erath

  2. TU Graz, Steyrergasse 30, 8010, Graz, Austria

    Günther Of

  3. University of Delaware, 532 Ewing Hall, Newark, 19716, USA

    Francisco-Javier Sayas

Authors
  1. Christoph Erath
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  2. Günther Of
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  3. Francisco-Javier Sayas
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Correspondence to Christoph Erath.

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Erath, C., Of, G. & Sayas, FJ. A non-symmetric coupling of the finite volume method and the boundary element method. Numer. Math. 135, 895–922 (2017). https://doi.org/10.1007/s00211-016-0820-3

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  • DOI: https://doi.org/10.1007/s00211-016-0820-3

Mathematics Subject Classification

  • 65N08
  • 65N38
  • 65N12
  • 65N15