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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C. Bernardi, Optimal finite-element interpolation on curved domains. SIAM J. Numer. Anal. 26(5), 1212–1240 (1989)
H. Egger, C. Erath, R. Schorr, On the non-symmetric coupling method for parabolic-elliptic interface problems. Preprint (2017). arXiv:1711.08487
C. Elliot, T. Ranner, Finite element analysis for a coupled bulk-surface partial differential equation. IMA J. Numer. Anal. 33(2), 377–402 (2013)
C. Johnson, J.-C. Nédélec, On the coupling of boundary integral and finite element methods. Math. Comput. 35(152), 1063–1079 (1987)
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)
R.C. MacCamy, M. Suri, A time-dependent interface problem for two-dimensional eddy currents. Quart. Appl. Math. 44(4), 675–690 (1987)
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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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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DOI: https://doi.org/10.1007/978-3-319-96415-7_94
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