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Numerische Mathematik

, Volume 130, Issue 2, pp 199–223 | Cite as

Stability of symmetric and nonsymmetric FEM–BEM couplings for nonlinear elasticity problems

  • M. Feischl
  • T. FührerEmail author
  • M. Karkulik
  • D. Praetorius
Article

Abstract

We consider symmetric as well as non-symmetric coupling formulations of FEM and BEM in the frame of nonlinear elasticity problems. In particular, the Johnson-Nédélec coupling is analyzed. We prove that these coupling formulations are well-posed and allow for unique Galerkin solutions if standard discretizations by piecewise polynomials are employed. Unlike prior works, our analysis does neither rely on an interior Dirichlet boundary to tackle the rigid body motions nor on any assumption on the mesh-size of the discretization used.

Mathematics Subject Classification

65N30 65N15 65N38 

Notes

Acknowledgments

The research of the authors is supported through the FWF research project Adaptive Boundary Element Method, see http://www.asc.tuwien.ac.at/abem/, funded by the Austrian Science Fund (FWF) under grant P21732, as well as through the Innovative Projects Initiative of Vienna University of Technology. This support is thankfully acknowledged. The authors thank Ernst P. Stephan (University of Hannover) and Heiko Gimperlein (Heriot-Watt University Edinburgh) for fruitful discussions and careful revisions of earlier versions of this manuscript. Moreover, we thank Francisco-Javier Sayas (University of Delaware) for some hint on the simplification of the proof of Theorem 2.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • M. Feischl
    • 1
  • T. Führer
    • 1
    Email author
  • M. Karkulik
    • 2
  • D. Praetorius
    • 1
  1. 1.Institute for Analysis and Scientific ComputingVienna University of TechnologyWienAustria
  2. 2.Facultad de MatemáticasPontificia Universidad Católica de ChileSantiagoChile

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