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European Conference on Numerical Mathematics and Advanced Applications

ENUMATH 2017: Numerical Mathematics and Advanced Applications ENUMATH 2017 pp 993–1001Cite as

A Simple Boundary Approximation for the Non-symmetric Coupling of the Finite Element Method and the Boundary Element Method for Parabolic-Elliptic Interface Problems

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

Abstract

The non-symmetric coupling for parabolic-elliptic interface problems on Lipschitz domains was recently analysed in Egger et al. (On the non-symmetric coupling method for parabolic-elliptic interface problems, preprint, 2017, arXiv:1711.08487). In Egger et al. (2017, Section 5) a classical FEM-BEM discretisation analysis was provided, but only with polygonal boundaries. In this short paper we will look at the case where the boundary is smooth. We introduce a polygonal approximation of the domain and compute the FEM-BEM coupling on this approximation. Note that the original quasi-optimality cannot be achieved. However, we are able to show a first order convergence result for lowest order FEM-BEM.

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References

  1. C. Bernardi, Optimal finite-element interpolation on curved domains. SIAM J. Numer. Anal. 26(5), 1212–1240 (1989)

    CrossRef  MathSciNet  Google Scholar 

  2. H. Egger, C. Erath, R. Schorr, On the non-symmetric coupling method for parabolic-elliptic interface problems. Preprint (2017). arXiv:1711.08487

    Google Scholar 

  3. C. Elliot, T. Ranner, Finite element analysis for a coupled bulk-surface partial differential equation. IMA J. Numer. Anal. 33(2), 377–402 (2013)

    CrossRef  MathSciNet  Google Scholar 

  4. C. Johnson, J.-C. Nédélec, On the coupling of boundary integral and finite element methods. Math. Comput. 35(152), 1063–1079 (1987)

    CrossRef  MathSciNet  Google Scholar 

  5. M. Le Roux, Méthode d’éléments finis pour la résolution numérique de problèmes extérieurs en dimension 2. R.A.I.R.O. Analyse numérique 11(1), 27–60 (1977)

    Google Scholar 

  6. R.C. MacCamy, M. Suri, A time-dependent interface problem for two-dimensional eddy currents. Quart. Appl. Math. 44(4), 675–690 (1987)

    CrossRef  MathSciNet  Google Scholar 

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Acknowledgements

This work is supported by the Excellence Initiative of the German Federal and State Governments and the Graduate School of Computational Engineering at TU Darmstadt. The authors would also like to thank Herbert Egger (TU Darmstadt) for pointing out this topic.

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Authors and Affiliations

  1. Graduate School of Computational Engineering, TU Darmstadt, Darmstadt, Germany

    Christoph Erath & Robert Schorr

  2. Department of Mathematics, TU Darmstadt, Darmstadt, Germany

    Christoph Erath & Robert Schorr

Authors
  1. Christoph Erath
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  2. Robert Schorr
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Corresponding author

Correspondence to Robert Schorr .

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Editors and Affiliations

  1. University of Bergen, Bergen, Norway

    Prof. Dr. Florin Adrian Radu

  2. University of Bergen, Bergen, Norway

    Dr. Kundan Kumar

  3. University of Bergen, Bergen, Norway

    Prof. Inga Berre

  4. University of Bergen, Bergen, Norway

    Prof. Dr. Jan Martin Nordbotten

  5. Hasselt University, Diepenbeek, Belgium

    Prof. Dr. Iuliu Sorin Pop

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Erath, C., Schorr, R. (2019). A Simple Boundary Approximation for the Non-symmetric Coupling of the Finite Element Method and the Boundary Element Method for Parabolic-Elliptic Interface Problems. 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_94

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