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

  • Christoph Erath
  • Robert SchorrEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)


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.



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.


  1. 1.
    C. Bernardi, Optimal finite-element interpolation on curved domains. SIAM J. Numer. Anal. 26(5), 1212–1240 (1989)MathSciNetCrossRefGoogle Scholar
  2. 2.
    H. Egger, C. Erath, R. Schorr, On the non-symmetric coupling method for parabolic-elliptic interface problems. Preprint (2017). arXiv:1711.08487Google Scholar
  3. 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)MathSciNetCrossRefGoogle Scholar
  4. 4.
    C. Johnson, J.-C. Nédélec, On the coupling of boundary integral and finite element methods. Math. Comput. 35(152), 1063–1079 (1987)MathSciNetCrossRefGoogle Scholar
  5. 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. 6.
    R.C. MacCamy, M. Suri, A time-dependent interface problem for two-dimensional eddy currents. Quart. Appl. Math. 44(4), 675–690 (1987)MathSciNetCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Graduate School of Computational EngineeringTU DarmstadtDarmstadtGermany
  2. 2.Department of MathematicsTU DarmstadtDarmstadtGermany

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